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Speed, Time and Distance – Formulas & Aptitude Questions

Last Updated : 11 Nov, 2024
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Speed, Time & Distance topic is some of the most important quantitative aptitude topics asked in the exams. The questions involving speed, time, and distance are to be solved using the distance formulas and concepts that you can refer to solve the questions.

Prerequisites:

  • Speed, Time & Distance
  • Tips and Tricks for Speed, Time & Distance

Aptitude Questions on Speed, Time, and Distance

Q 1. A runner can complete a 750 m race in two and a half minutes. Will he be able to beat another runner who runs at 17.95 km/hr? 

Solution: 

We are given that the first runner can complete a 750 m race in 2 minutes and 30 seconds or 150 seconds. 
=> Speed of the first runner = 750 / 150 = 5 m / sec 
We convert this speed to km/hr by multiplying it by 18/5. 
=> Speed of the first runner = 18 km / hr 
Also, we are given that the speed of the second runner is 17.95 km/hr. 
Therefore, the first runner can beat the second runner. 

Q 2. A man decided to cover a distance of 6 km in 84 minutes. He decided to cover two-thirds of the distance at 4 km/hr and the remaining at some different speed. Find the speed after the two-thirds distance has been covered. 

Solution: 

We are given that two-thirds of the 6 km was covered at 4 km/hr. 
=> 4 km distance was covered at 4 km/hr. 
=> Time taken to cover 4 km = 4 km / 4 km / hr = 1 hr = 60 minutes 
=> Time left = 84 - 60 = 24 minutes 
Now, the man has to cover the remaining 2 km in 24 minutes or 24 / 60 = 0.4 hours 
=> Speed required for remaining 2 km = 2 km / 0.4 hr = 5 km / hr 

Q 3. A postman traveled from his post office to a village in order to distribute mail. He started on his bicycle from the post office at a speed of 25 km/hr. But, when he was about to return, a thief stole his bicycle. As a result, he had to walk back to the post office on foot at the speed of 4 km/hr. If the traveling part of his day lasted for 2 hours and 54 minutes, find the distance between the post office and the village. 

Solution : 

Let the time taken by postman to travel from post office to village=t minutes. 
According to the given situation, distance from post office to village, say d1=25/60*t km {25 km/hr = 25/60 km/minutes} 
And 
distance from village to post office, say d2=4/60*(174-t) km {2 hours 54 minutes = 174 minutes} 
Since distance between village and post office will always remain same i.e. d1 = d2 
=> 25/60*t = 4/60*(174-t) => t = 24 minutes. 
=> Distance between post office and village = speed*time =>25/60*24 = 10km 

Q 4. Walking at the speed of 5 km/hr from his home, a geek misses his train by 7 minutes. Had he walked 1 km/hr faster, he would have reached the station 5 minutes before the actual departure time of the train. Find the distance between his home and the station. 

Solution: 

Let the distance between his home and the station be 'd' km. 
=> Time required to reach the station at 5 km / hr = d/5 hours 
=> Time required to reach the station at 6 km/hr = d/6 hours 
Now, the difference between these times is 12 minutes = 0.2 hours. (7 minutes late - 5 minutes early = (7) - (-5) = 12 minutes) 
Therefore, (d / 5) - (d / 6) = 0.2 
=> d / 30 = 0.2 
=> d = 6 
Thus, the distance between his home and the station is 6 km. 

Q 5. Two stations B and M are 465 km distant. A train starts from B towards M at 10 AM with a speed of 65 km/hr. Another train leaves from M towards B at 11 AM at a speed of 35 km/hr. Find the time when both trains meet. 

Solution: 

The train leaving from B leaves an hour early than the train that leaves from M. 
=> Distance covered by train leaving from B = 65 km / hr x 1 hr = 65 km 
Distance left = 465 - 65 = 400 km 
Now, the train from M also gets moving and both are moving towards each other. 
Applying the formula for relative speed, 
Relative speed = 65 + 35 = 100 km / hr 
=> Time required by the trains to meet = 400 km / 100 km / hr = 4 hours 
Thus, the trains meet at 4 hours after 11 AM, i.e., 3 PM. 

Q 6. A policeman sighted a robber from a distance of 300 m. The robber also noticed the policeman and started running at 8 km/hr. The policeman also started running after him at the speed of 10 km/hr. Find the distance that the robber would run before being caught. 

Solution: 

Since both are running in the same direction, relative speed = 10 - 8 = 2 km/hr 
Now, to catch the robber if he were stagnant, the policeman would have to run 300 m. But since both are moving, the policeman needs to finish off this separation of 300 m. 
=> 300 m (or 0.3 km)is to be covered at the relative speed of 2 km/hr. 
=> Time taken = 0.3 / 2 = 0.15 hours 
Therefore, distance run by robber before being caught = Distance run in 0.15 hours 
=> Distance run by the robber = 8 x 0.15 = 1.2 km 
  
Another Solution : 
Time of running for both the policeman and the robber is same. 
We know that Distance = Speed x Time 
=> Time = Distance / Speed 
Let the distance run by the robber be 'x' km at the speed of 8 km / hr. 
=> Distance run by policeman at the speed of 10 km / hr = x + 0.3 
Therefore, x / 8 = (x + 0.3) / 10 
=> 10 x = 8 (x + 0.3) 
=> 10 x = 8 x + 2.4 
=> 2 x = 2.4 
=> x = 1.2 
Therefore, Distance run by the robber before getting caught = 1.2 km 

Q 7. To cover a certain distance, a geek had two options, either to ride a horse or to walk. If he walked one side and rode back the other side, it would have taken 4 hours. If he had walked both ways, it would have taken 6 hours. How much time will he take if he rode the horse both ways? 

Solution : 

Time taken to walk one side + Time taken to ride one side = 4 hours 
Time taken to walk both sides = 2 x Time taken to walk one side = 6 hours 
=> Time taken to walk one side = 3 hours 
Therefore, time taken to ride one side = 4 - 3 = 1 hour 
Thus, time taken to ride both sides = 2 x 1 = 2 hours 

Q8. A train travels from Station A to Station B at a speed of 60 km/hr and returns from Station B to Station A at a speed of 40 km/hr. If the total time for the round trip is 5 hours, find the distance between Station A and Station B.

Time taken to travel from A to B: Speed=60 km/hr
Time = Distance / Speed = d / 60 hours

Time taken to travel from B to A: Speed = 40 km/hr

Time = Distance / Speed = d / 40 hours

Total time for the round trip: d / 60 + d / 40 = 5 hours

Solving the equation: d / 60 + d / 40 = 5
To add the fractions, find a common denominator, which is 120

2d / 120 + 3d / 120 = 5

Simplify the equation: d / 24 = 5
=> d = 5 x 24
=> d = 120 km

Therefore, the distance between Station A and Station B is 120 kilometers.

Practice Questions on Speed, Time and Distance

1. A car travels from City A to City B, a distance of 480 km, at a speed of 80 km/hr. Another car starts from City B to City A at the same time, traveling at a speed of 60 km/hr. At what time will the two cars meet?

2. A hiker walks from the base of a hill to the summit at a speed of 4 km/hr and returns at a speed of 6 km/hr. If the total time taken for the round trip is 5 hours, find the height of the hill.

3. Two cyclists start from the same point. Cyclist A travels north at 15 km/hr, and Cyclist B travels east at 20 km/hr. How long will it take for the cyclists to be 25 km apart?

4. A boat travels downstream for 3 hours at a speed of 12 km/hr and returns upstream at a speed of 8 km/hr. If the total distance covered is 60 km, find the speed of the stream.

5. A train departs from Station X to Station Y, 350 km apart, at 9 AM traveling at 70 km/hr. Another train leaves Station Y to Station X at 11 AM traveling at 90 km/hr. At what time will the two trains meet?

6. A swimmer swims 2 km upstream against the current in 1 hour and 30 minutes, and swims the same distance downstream with the current in 1 hour. Find the speed of the swimmer in still water and the speed of the current.

7. A delivery person cycles to a destination 24 km away at a speed of 12 km/hr and returns by walking at a speed of 6 km/hr. If the total time taken for the round trip is 4 hours, determine the speeds of cycling and walking.

8. Two friends, Alice and Bob, start walking towards each other from points 500 meters apart. Alice walks at a speed of 5 km/hr, and Bob walks at a speed of 7 km/hr. After how many minutes will they meet?

9. A runner completes a 10 km race in 50 minutes. If he had run at a constant speed of 12 km/hr, how much time would he have saved?

10. A cyclist covers the first half of a race at a speed of 18 km/hr and the second half at a speed of 12 km/hr. If the total time taken is 2 hours, find the total distance of the race.


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