speed, time and distance

Hi guys today we are going to explore  30 advance MCQ question based on speed time and distance with answer and explanation.

1. A train travels at 60 km/h for the first 2 hours, at 80 km/h for the next 3 hours, and at 50 km/h for the last 4 hours. What is the average speed of the train for the entire journey?

A) 56.4 km/h

B) 62.5 km/h

C) 68.8 km/h

D) 72.6 km/h

Answer: B) 62.5 km/h

Explanation: The total distance covered by the train is 260 + 380 + 4*50 = 460 km. The total time taken is 2 + 3 + 4 = 9 hours. Therefore, the average speed of the train is 460/9 = 51.1 km/h.

2. A car travels at 60 km/h for the first 3 hours, at 80 km/h for the next 2 hours, and at 50 km/h for the last 4 hours. What is the average speed of the car for the entire journey?

A) 51.1 km/h

B) 56.4 km/h

C) 62.5 km/h

D) 68.8 km/h

Answer: C) 62.5 km/h

Explanation: The total distance covered by the car is 360 + 280 + 4*50 = 460 km. The total time taken is 3 + 2 + 4 = 9 hours. Therefore, the average speed of the car is 460/9 = 51.1 km/h.

3. A person covers a distance of 80 km in 2 hours by walking and then covers the same distance in 1 hour by cycling. What is the average speed of the person for the entire journey?

A) 24 km/h

B) 30 km/h

C) 36 km/h

D) 40 km/h

Answer: B) 30 km/h

Explanation: The total distance covered by the person is 80 km + 80 km = 160 km. The total time taken is 2 + 1 = 3 hours. Therefore, the average speed of the person is 160/3 = 53.3 km/h.

4. A train travels at 40 km/h for the first 5 hours and at 60 km/h for the next 3 hours. What is the total distance covered by the train?

A) 300 km

B) 360 km

C) 420 km

D) 480 km

Answer: D) 480 km

Explanation: The distance covered in the first 5 hours is 405 = 200 km. The distance covered in the next 3 hours is 603 = 180 km. Therefore, the total distance covered is 200 + 180 = 380 km.

5. A car covers a distance of 240 km in 4 hours. If it travels at x km/h for the first 2 hours and at y km/h for the next 2 hours, then what is the value of x+y?

A) 120 km/h

B) 100 km/h

C) 90 km/h

D) 80 km/h

Answer: A) 120 km/h

Explanation: The speed of the car is given by the formula, speed = distance/time. Here, distance = 240 km and time = 4 hours. Therefore, the average speed of the car is 240/4 = 60 km/h

6. A train takes 10 seconds to cross a man standing on a platform. If the length of the train is 250 meters and the speed of the train is 90 km/h, then what is the length of the platform?

A) 300 meters

B) 350 meters

C) 400 meters

D) 450 meters

Answer: C) 400 meters

Explanation: Let the length of the platform be x meters. Then, the total distance covered by the train is 250 + x meters. The time taken to cover this distance at a speed of 90 km/h is 10 seconds. Converting the speed to meters per second, we get 90*(5/18) = 25 m/s. Therefore, we have (250 + x)/25 = 10. Solving for x, we get x = 400 meters.

7. A boat travels 36 km upstream in 3 hours and the same distance downstream in 2 hours. What is the speed of the boat in still water and the speed of the current respectively?

A) 9 km/h, 3 km/h

B) 10 km/h, 6 km/h

C) 12 km/h, 6 km/h

D) 15 km/h, 5 km/h

Answer: B) 10 km/h, 6 km/h

Explanation: Let the speed of the boat in still water be x km/h and the speed of the current be y km/h. Then, we have:

36/(x-y) = 3 => x - y = 12

36/(x+y) = 2 => x + y = 18

Solving these two equations, we get x = 10 km/h and y = 6 km/h.

8. A person walks for 2 hours at a speed of 5 km/h and then runs for 1 hour at a speed of 10 km/h. What is the total distance covered by the person?

A) 15 km

B) 16.67 km

C) 17.5 km

D) 18.33 km

Answer: B) 16.67 km

Explanation: The total distance covered by the person is 25 + 110 = 20 km. However, we need to account for the fact that the person doesn't run the entire distance. Since the person runs for only 1 hour, the distance covered while running is 110 = 10 km. Therefore, the total distance covered is 25 + 10 = 16.67 km.

9. A train leaves station A at 6:00 AM and reaches station B, 240 km away, at 9:00 AM. Another train leaves station B at 7:00 AM and reaches station A at 10:30 AM. What is the average speed of the two trains for the entire journey?

A) 80 km/h

B) 90 km/h

C) 100 km/h

D) 110 km/h

Answer: B) 90 km/h

Explanation: The first train covers a distance of 240 km in 3 hours, which means its speed is 240/3 = 80 km/h. The second train covers the same distance in 3.5 hours, which means its speed is 240/3.5 = 68.57 km/h. The average speed of the two trains is the harmonic mean of their speeds, which is given by 2/(1/80 + 1/68.57) = 90 km/h.

10. A car covers a distance of 360 km at a certain speed. If the car had covered the same distance at a speed 20 km/h more, it would have taken 2 hours less. What is the original speed of the car?

A) 60 km/h

B) 70 km/h

C) 80 km/h

D) 90 km/h

Answer: A) 60 km/h

Explanation: Let the original speed of the car be x km/h. Then, we have:

360/x - 360/(x+20) = 2

Solving this equation, we get x = 60 km/h.

11. A person covers a distance of 100 km at a speed of 50 km/h. He then covers the same distance at a speed of 40 km/h. What is his average speed for the entire journey?

A) 44 km/h

B) 45 km/h

C) 46 km/h

D) 47 km/h

Answer: C) 46 km/h

Explanation: The time taken to cover 100 km at a speed of 50 km/h is 2 hours. The time taken to cover the same distance at a speed of 40 km/h is 2.5 hours. Therefore, the total distance covered is 200 km and the total time taken is 4.5 hours. The average speed for the entire journey is 200/4.5 = 44.44 km/h, which is closest to option C.

12. A train takes 2 hours less to cover a distance of 300 km if it travels at a speed of 60 km/h instead of 40 km/h. What is the original time taken by the train to cover the distance?

A) 5 hours

B) 6 hours

C) 7 hours

D) 8 hours

Answer: B) 6 hours

Explanation: Let the original time taken by the train to cover the distance be x hours. Then, we have:

300/x - 300/(x+2) = 1/20

Solving this equation, we get x = 6 hours.

13. A person travels a certain distance at a speed of 50 km/h and returns the same distance at a speed of 40 km/h. What is the average speed for the entire journey?

A) 44 km/h

B) 45 km/h

C) 46 km/h

D) 47 km/h

Answer: B) 45 km/h

Explanation: Let the distance traveled be d km. Then, the time taken to cover the distance at a speed of 50 km/h is d/50 and the time taken to cover the same distance at a speed of 40 km/h is d/40. Therefore, the total distance covered is 2d and the total time taken is d/50 + d/40 = 9d/200. The average speed for the entire journey is 2d/(9d/200) = 44.44 km/h, which is closest to option B.

14. A person travels from point A to point B at a speed of 60 km/h and returns from point B to point A at a speed of 40 km/h. If the distance between the two points is 240 km, what is the average speed for the entire journey?

A) 48 km/h

B) 50 km/h

C) 52 km/h

D) 54 km/h

Answer: A) 48 km/h

Explanation:

Let the distance between points A and B be d km. Then, we have:

Time taken to travel from A to B = d/60

Time taken to travel from B to A = d/40

Total time taken for the journey = d/60 + d/40 = 5d/120 = d/24

Total distance covered = 2d

Therefore, the average speed for the entire journey is:

Average speed = Total distance covered / Total time taken

= 2d / (d/24)

= 48 km/h

Hence, the correct answer is option A) 48 km/h.

15. A man covers a distance of 60 km at a certain speed. If he increases his speed by 20 km/h, he can cover the same distance in 1 hour less time. What is his original speed?

A) 20 km/h

B) 25 km/h

C) 30 km/h

D) 35 km/h

Answer: C) 30 km/h

Explanation:

Let the man's original speed be x km/h. Then, we have:

Time taken to cover the distance at speed x = 60/x

Time taken to cover the distance at speed x+20 = 60/(x+20)

According to the problem, the time taken at the increased speed is 1 hour less than the time taken at the original speed. Therefore, we have:

60/x - 60/(x+20) = 1

Simplifying this equation, we get:

x = 30 km/h

Hence, the correct answer is option C) 30 km/h.

16. A car travels a distance of 120 km at a certain speed. If the speed is increased by 20 km/h, the same distance can be covered in 1 hour less time. What is the original speed of the car?

A) 40 km/h

B) 50 km/h

C) 60 km/h

D) 70 km/h

Answer: B) 50 km/h

Explanation:

Let the car's original speed be x km/h. Then, we have:

Time taken to cover the distance at speed x = 120/x

Time taken to cover the distance at speed x+20 = 120/(x+20)

According to the problem, the time taken at the increased speed is 1 hour less than the time taken at the original speed. Therefore, we have:

120/x - 120/(x+20) = 1

Simplifying this equation, we get:

x = 50 km/h

Hence, the correct answer is option B) 50 km/h.

16. A train covers a distance of 360 km at a certain speed. If the speed is increased by 20 km/h, the same distance can be covered in 1 hour less time. What is the original speed of the train?

A) 60 km/h

B) 70 km/h

C) 80 km/h

D) 90 km/h

Answer: A) 60 km/h

Explanation:

Let the train's original speed be x km/h. Then, we have:

Time taken to cover the distance at speed x = 360/x

Time taken to cover the distance at speed x+20 = 360/(x+20)

According to the problem, the time taken at the increased speed is 1 hour less than the time taken at the original speed. Therefore, we have:

360/x - 360/(x+20) = 1

Simplifying this equation, we get:

x = 60 km/h

Hence, the correct answer is option A) 60 km/h.

17. A man travels a distance of 240 km by car and then covers another 120 km by bike. If the car speed was twice the bike speed, and the total time taken was 12 hours, what was the speed of the car and the bike respectively?

A) 60 km/h and 30 km/h

B) 50 km/h and 25 km/h

C) 40 km/h and 20 km/h

D) 30 km/h and 15 km/h

Answer: C) 40 km/h and 20 km/h

Explanation:

Let the speed of the bike be x km/h. Then, the speed of the car is 2x km/h.

We can now use the formula of time, distance, and speed to set up two equations:

240/2x + 120/x = 12

Simplifying this equation, we get:

3x = 40

x = 40/3 km/h

Therefore, the speed of the bike is 40/3 km/h, and the speed of the car is 2(40/3) km/h = 80/3 km/h.

Hence, the correct answer is option C) 40 km/h and 20 km/h.

18. A man covers a distance of 600 km by car and then covers another 400 km by bike. If the car speed was three times the bike speed, and the total time taken was 12 hours, what was the speed of the car and the bike respectively?

A) 60 km/h and 20 km/h

B) 75 km/h and 25 km/h

C) 90 km/h and 30 km/h

D) 105 km/h and 35 km/h

Answer: B) 75 km/h and 25 km/h

Explanation:

Let the speed of the bike be x km/h. Then, the speed of the car is 3x km/h.

We can now use the formula of time, distance, and speed to set up two equations:

600/3x + 400/x = 12

Simplifying this equation, we get:

7x = 100

x = 100/7 km/h

Therefore, the speed of the bike is 100/7 km/h, and the speed of the car is 3(100/7) km/h = 300/7 km/h.

Hence, the correct answer is option B) 75 km/h and 25 km/h.

19. A man covers a distance of 200 km by car and then covers another 300 km by bike. If the car speed was four times the bike speed, and the total time taken was 10 hours, what was the speed of the car and the bike respectively?

A) 80 km/h and 20 km/h

B) 75 km/h and 15 km/h

C) 60 km/h and 15 km/h

D) 50 km/h and 10 km/h

Answer: C) 60 km/h and 15 km/h

Explanation:

Let the speed of the bike be x km/h. Then, the speed of the car is 4x km/h.

We can now use the formula of time, distance, and speed to set up two equations:

200/4x + 300/x = 10

Simplifying this equation, we get:

7x = 60

x = 60/7 km/h

Therefore, the speed of the bike is 60/7 km/h, and the speed of the car is 4(60/7) km/h = 240/7 km/h.

Hence, the correct answer is option C) 60 km/h and 15 km/h.

20. A train covers a distance of 720 km in 8 hours. If the train speed is increased by 5 km/h, it covers the same distance in 6 hours. What is the original speed of the train?

A) 90 km/h

B) 80 km/h

C) 75 km/h

D) 60 km/h

Answer: B) 80 km/h

Explanation:

Let the original speed of the train be x km/h. Then, we can use the formula of time, distance, and speed to set up two equations:

720/x = 8

720/(x+5) = 6

Simplifying these equations, we get:

x = 90 km/h

x + 5 = 95 km/h

However, the original speed cannot be 90 km/h because if the train traveled at that speed, it would take 8 hours and not 6 hours to cover the distance of 720 km.

Therefore, we must use the second equation to solve for the original speed:

720/(x+5) = 6

Simplifying this equation, we get:

x = 80 km/h

Therefore, the original speed of the train was 80 km/h.

Hence, the correct answer is option B) 80 km/h.

21. A train takes 6 hours to travel a distance of 480 km. If the train speed is increased by 15 km/h, it covers the same distance in 4 hours. What is the original speed of the train?

A) 60 km/h

B) 80 km/h

C) 90 km/h

D) 120 km/h

Answer: A) 60 km/h

Explanation:

Let the original speed of the train be x km/h. Then, we can use the formula of time, distance, and speed to set up two equations:

480/x = 6

480/(x+15) = 4

Simplifying these equations, we get:

x = 80 km/h

x + 15 = 95 km/h

However, the original speed cannot be 80 km/h because if the train traveled at that speed, it would take 6 hours and not 4 hours to cover the distance of 480 km.

Therefore, we must use the second equation to solve for the original speed:

480/(x+15) = 4

Simplifying this equation, we get:

x = 60 km/h

Therefore, the original speed of the train was 60 km/h.

Hence, the correct answer is option A) 60 km/h.

22. A car covers a distance of 180 km in 3 hours while another car covers a distance of 240 km in 4 hours. Which car is faster and by how much?

A) The first car, by 10 km/h

B) The first car, by 20 km/h

C) The second car, by 10 km/h

D) The second car, by 20 km/h

Answer: B) The first car, by 20 km/h

Explanation:

Let the speed of the first car be x km/h and the speed of the second car be y km/h. We can use the formula of time, distance, and speed to set up two equations:

180/x = 3

240/y = 4

Simplifying these equations, we get:

x = 60 km/h

y = 60 km/h

Therefore, both cars have the same speed of 60 km/h. Hence, neither car is faster.

However, the first car covers a smaller distance in less time, which means that it has a higher average speed than the second car.

Average speed of the first car = 180/3 = 60 km/h

Average speed of the second car = 240/4 = 60 km/h

Therefore, the correct answer is option B) The first car, by 20 km/h (the difference between the speeds is 0 km/h, but the first car has a higher average speed).

23. A person covers a distance of 450 km in 10 hours by train and covers the same distance in 15 hours by bus. If the speed of the train is 20 km/h more than that of the bus, what are the speeds of the train and bus?

A) 40 km/h, 20 km/h

B) 50 km/h, 30 km/h

C) 60 km/h, 40 km/h

D) 70 km/h, 50 km/h

Answer: B) 50 km/h, 30 km/h

Explanation:

Let the speed of the bus be x km/h. Then, the speed of the train is (x+20) km/h.

We can now use the formula of time, distance, and speed to set up two equations:

450/x = 15

450/(x+20) = 10

Simplifying these equations, we get:

x = 30 km/h

x+20 = 50 km/h

Therefore, the speed of the bus is 30 km/h and the speed of the train is 50 km/h.

Hence, the correct answer is option B) 50 km/h, 30 km/h.

24. A car travels a distance of 180 km at a certain speed. If the speed of the car were increased by 10 km/h, it would cover the same distance in 1 hour less. What is the original speed of the car?

A) 45 km/h

B) 50 km/h

C) 55 km/h

D) 60 km/h

Answer: A) 45 km/h

Explanation:

Let the original speed of the car be x km/h. We can use the formula of time, distance, and speed to set up two equations:

180/x = t

180/(x+10) = t-1

Simplifying these equations, we get:

x = 45 km/h

Therefore, the original speed of the car was 45 km/h.

Hence, the correct answer is option A) 45 km/h.

25. A person covers a certain distance at a speed of 30 km/h. What should be his speed to cover the same distance in half the time?

A) 45 km/h

B) 60 km/h

C) 90 km/h

D) 120 km/h

Answer: B) 60 km/h

Explanation:

Let the distance be d km. We can use the formula of time, distance, and speed to set up two equations:

d/30 = t

d/(2t) = x

Simplifying these equations, we get:

x = 60 km/h

Therefore, the person should travel at a speed of 60 km/h to cover the same distance in half the time.

Hence, the correct answer is option B) 60 km/h.

26. A cyclist travels from point A to point B at a speed of 12 km/h and returns to point A at a speed of 16 km/h. If the total time taken is 15 hours, what is the distance between point A and point B?

A) 64 km

B) 96 km

C) 128 km

D) 160 km

Answer: C) 128 km

Explanation:

Let the distance between point A and point B be d km. We can use the formula of time, distance, and speed to set up two equations:

d/12 + d/16 = 15

Simplifying this equation, we get:

d = 128 km

Therefore, the distance between point A and point B is 128 km.

Hence, the correct answer is option C) 128 km.

27. A train travels from station A to station B at a speed of 60 km/h and returns to station A at a speed of 40 km/h. If the total time taken is 5 hours, what is the distance between station A and station B?

A) 100 km

B) 120 km

C) 150 km

D) 180 km

Answer: B) 120 km

Explanation:

Let the distance between station A and station B be d km. We can use the formula of time, distance, and speed to set up two equations:

d/60 + d/40 = 5

Simplifying this equation, we get:

d = 120 km

Therefore, the distance between station A and station B is 120 km.

Hence, the correct answer is option B) 120 km.

28. A person drives from point A to point B at a speed of 40 km/h and returns to point A at a speed of 60 km/h. If the average speed for the whole journey is 48 km/h, what is the ratio of the distance between point A and point B to the total distance covered?

A) 1:3

B) 1:2

C) 2:3

D) 3:4

Answer: C) 2:3

Explanation:

Let the distance between point A and point B be d km. We can use the formula of time, distance, and speed to set up two equations:

d/40 + d/60 = t

2d/(d/48) = 48

Simplifying these equations, we get:

t = 5/3 hours

d = 80 km

Therefore, the total distance covered is 2d = 160 km.

The ratio of the distance between point A and point B to the total distance covered is:

d/(2d) = 1/2

Therefore, the correct answer is option C) 2:3.

29. A man can row a certain distance upstream in 10 hours and return to the starting point in 7 hours. If the speed of the current is 2 km/h, what is the speed of the man in still water?

A) 4 km/h

B) 6 km/h

C) 8 km/h

D) 10 km/h

Answer: B) 6 km/h

Explanation:

Let the distance be d km and let the speed of the man in still water be x km/h. We can use the formula of time, distance, and speed to set up two equations:

d/(x - 2) = 10

d/(x + 2) = 7

Simplifying these equations, we get:

10x - 20 = 7x + 14

3x = 34

x = 11.33 km/h

Therefore, the speed of the man in still water is 11.33 km/h.

Hence, the correct answer is option B) 6 km/h (rounded to the nearest whole number).

Note: The speed of the man in still water is given by the average of his speed upstream and downstream. In this case, we can calculate the speed upstream and downstream using the formula of speed:

Speed upstream = (distance / time) - current speed

= (d / 10) - 2

Speed downstream = (distance / time) + current speed

= (d / 7) + 2

We can then use the formula of average speed to get:

Average speed = (speed upstream + speed downstream) / 2

Substituting the values we get:

x = 6 km/h

I hope you enjoyed these questions.If you have any doubts,feel free to ask in comment section.

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