Practice Time and Distance questions covering speed, distance, and time formulas, average speed, and relative speed problems for Quantitative Aptitude.
Question 1
A train covered the first 5 km of its journey at a speed of 30 km/hr and the next 15 km at a speed of 45 km/hr. The average speed of the train was:
Explanation
Time for first leg = 530 = 16 hr
Time for second leg = 1545 = 13 hr
Total time = 16 + 13 = 12 hr. Total distance = 20 km
Average speed = 2012 = 40 km/hr
Time for second leg = 1545 = 13 hr
Total time = 16 + 13 = 12 hr. Total distance = 20 km
Average speed = 2012 = 40 km/hr
Question 2
A man travels from Delhi to Agra at an average speed of 30 km per hour and back at an average speed of 60 km per hour. What is the average speed for the whole journey?
Explanation
For an equal-distance two-leg journey, average speed = 2 × s1 × s2s1 + s2
= 2 × 30 × 6030 + 60 = 360090 = 40 km/hr
= 2 × 30 × 6030 + 60 = 360090 = 40 km/hr
Question 3
Aman walks a certain distance at a certain speed. If he walks 12 km an hour faster, he takes 1 hour less. But if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.
Explanation
Let original speed = s, time = t, distance = d = st.
(s + 0.5)(t - 1) = d ⇒ -s + 0.5t - 0.5 = 0 ⇒ t = 2s + 1
(s - 1)(t + 3) = d ⇒ 3s - t - 3 = 0 ⇒ t = 3s - 3
Equating: 2s + 1 = 3s - 3 ⇒ s = 4
t = 2(4) + 1 = 9
Distance = st = 4 × 9 = 36 km
(s + 0.5)(t - 1) = d ⇒ -s + 0.5t - 0.5 = 0 ⇒ t = 2s + 1
(s - 1)(t + 3) = d ⇒ 3s - t - 3 = 0 ⇒ t = 3s - 3
Equating: 2s + 1 = 3s - 3 ⇒ s = 4
t = 2(4) + 1 = 9
Distance = st = 4 × 9 = 36 km
Question 4
A lady travels at a speed of 20 km/h and returns at a quicker speed. If her average speed for the whole journey is 24 km/h, find the speed of the return journey (in km/h).
Explanation
For a round trip with speeds s1 and s2, average speed = 2 × s1 × s2s1 + s2
2 × 20 × s220 + s2 = 24
40s2 = 24(20 + s2)
40s2 = 480 + 24s2
16s2 = 480
s2 = 30
2 × 20 × s220 + s2 = 24
40s2 = 24(20 + s2)
40s2 = 480 + 24s2
16s2 = 480
s2 = 30
Question 5
How many seconds does Puja take to cover a distance of 500 m, if she runs at a speed of 30 km/hr?
Explanation
Speed = 30 × 518 = 253 m/s. Time = 500 × 325 = 60 sec.
Question 6
A cyclist covers a distance of 800 meters in 4 minutes 20 seconds. What is the speed in km/hr of the cyclist?
Explanation
Time = 4 min 20 sec = 260 sec. Speed = 800260 = 3.077 m/s. Converting to km/hr: 3.077 × 185 ≈ 11.08 km/hr.
Question 7
A man walking at the rate of 6 km/hr crosses a bridge in 15 minutes. The length of the bridge is ______.
Explanation
Speed = 6 × 518 = 53 m/s. Time = 15 × 60 = 900 sec. Distance = Speed × Time = 53 × 900 = 1500 m.
Question 8
Two girls move in opposite directions, one from A to B and other from B to A. The girl from A reaches the destination in 16 hrs and girl from B reaches her destination in 25 hrs, after having met. If former's speed is 25 km/hr, what will be the speed of latter?
Explanation
If two bodies moving toward each other reach their destinations in ta and tb hours respectively after meeting, then SaSb = √tb√ta. Here ta = 16, tb = 25, Sa = 25 km/hr: Sb = Sa × √ta√tb = 25 × 45 = 20 km/hr.
Question 9
Two buses start at the same time, one from P to Q and the other from Q to P. If both buses reach after 4 hours and 16 hours at Q and P respectively after they cross each other, what would be the ratio of speeds of the bus starting from P and that of the one starting from point Q?
Explanation
Using SPSQ = √tP√tQ, where tP = 16 hrs (Q-bus's time to reach P) and tQ = 4 hrs (P-bus's time to reach Q): SPSQ = √16√4 = 42 = 2 : 1.
Question 10
An aeroplane flying 800 km covers the first 200 km at the rate of 200 km/hr, the second 200 km at 400 km/hr, the third 200 km at 600 km / hr & last 200 km at the rate of 800 km/hr. Determine the average speed of the aeroplane.
Explanation
Total distance = 4 × 200 = 800 km.
Total time = 200200 + 200400 + 200600 + 200800 = 1 + 12 + 13 + 14 = 2512 hrs.
Average speed = 800 × 1225 = 384 km/hr.
Total time = 200200 + 200400 + 200600 + 200800 = 1 + 12 + 13 + 14 = 2512 hrs.
Average speed = 800 × 1225 = 384 km/hr.
Question 11
Jennifer travels first 4 hours of her journey at a speed of 80 miles/hr and the remaining distance in 6 hours at a speed of 30 miles/hr. What is her average speed in miles/hr?
Explanation
Total distance = (80 × 4) + (30 × 6) = 320 + 180 = 500 miles. Total time = 4 + 6 = 10 hours. Average speed = 50010 = 50 miles/hr.
Question 12
A man covers the first 458 km of his journey in 450 minutes and the remaining 372 km in 560 minutes. What is the average speed of the man?
Explanation
Total distance = 458 + 372 = 830 km. Total time = 450 + 560 = 1010 minutes = 101060 ≈ 16.83 hours.
Average speed = 83016.83 ≈ 49.3 km/hr.
Average speed = 83016.83 ≈ 49.3 km/hr.
Question 13
Two boys start running from the same place in opposite directions. One goes towards east at 18 km per hour and the other goes towards west at 20 km per hour. What time do they take to be 76 km apart?
Explanation
Since they move in opposite directions, their relative speed = 18 + 20 = 38 km/hr. Time = 7638 = 2 hours.
Question 14
Abhishek walks a certain distance and rides back, taking a total time of 35 minutes. Abhishek could walk both ways in 30 minutes. How long would it take him to ride both ways?
Explanation
Walking both ways takes 30 minutes, so walking one way takes 15 minutes. Since walking one way + riding one way = 35 minutes, riding one way = 35 - 15 = 20 minutes. Riding both ways = 2 × 20 = 40 minutes.
Question 15
A man goes up a hill at 18 kmph and comes down at 24 kmph along the same path. What is his average speed?
Explanation
For a round trip with equal distances at two different speeds, average speed = 2 × 18 × 2418 + 24 = 86442 ≈ 20.57 kmph.
Question 16
The ratio of speeds of A and B is 1:4. If B covers a distance in 20 minutes, A will cover it in:
Explanation
For the same distance, time is inversely proportional to speed. Since A's speed is 14 of B's speed, A takes 4 times as long as B. A's time = 20 × 4 = 80 minutes.
Question 17
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 km away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at stations. The speed of the car is:
Explanation
Let car speed = v. Train speed = 1.5v. Train's moving time = 75/1.5v = 50/v. Since the train's total elapsed time (including the 12.5 min stop) equals the car's travel time: 50/v + 12.560 = 75/v, giving 12.560 = 25/v, so v = 120 km/hr.
Question 18
A cyclist covers a distance of 900m in 4 min 30 sec. What is the speed in km/h of the cyclist?
Explanation
Speed = 900m / 270sec = 3.33 m/s = 12 km/h.
Question 19
Peter can cover a certain distance in 1 hour and 4 minutes by covering one-third the distance at 5 km/h and the rest at 6 km/h. Find the total distance.
Explanation
Let distance = D. Time = (D/3)/5 + (2D/3)/6 = D/15+D/9 = 8D/45. Setting 8D/45 = 6460 hr gives D = 6 km.
Question 20
A man travelled from the village to the post-office at the rate of 20 km/h and walked back at the rate of 2 km/h. If the whole journey took 4 hours 24 minutes, find the distance of the post-office from the village.
Explanation
Let distance = d. d/20 + d/2 = 4.4 hr, giving d(1120) = 4.4, so d = 8 km.
Question 21
An airplane flies along the four sides of a square field at speeds of 100, 150, 200 and 250 km/h. Find the average speed of the plane around the field.
Explanation
Average speed = 4L / (L/100+L/150+L/200+L/250) = 4/(773000) = 1200077 ≈ 155.8 km/h, which does not match any listed option, so the answer is None of these.
Question 22
Running at 56 of its usual speed, a train is 20 min too late. Find its usual time to cover the journey.
Explanation
Extra time = T(65-1) = T/5 = 20 min, so T=100 min, which does not match any listed option, so the answer is None of these.
Question 23
A car is running at a speed of 110 km/h. What is the distance covered in 10 seconds?
Explanation
110 km/h = 30.56 m/s. Distance in 10 sec = 305.6 meters.
Question 24
The speed of a car increases by 4 km/h after every hour. If the distance travelled in the first hour was 40 km, what is the total distance covered in 10 hours?
Explanation
This is an arithmetic series: first term=40, common difference=4, n=10. Sum = 102 × (2 × 40+9 × 4) = 5 × 116 = 580 km.
Question 25
A train covers a distance of 12 km in 12 min. If its speed is decreased by 10 km/h, the time taken by it to cover the same distance will be:
Explanation
Original speed = 12 km12 min = 60 km/h. New speed = 60 - 10 = 50 km/h.
New time = 1250 hr = 0.24 hr = 14.4 min.
New time = 1250 hr = 0.24 hr = 14.4 min.
