# Time and Distance - Aptitude Questions and Answers - RejinpaulPlacement

8.
Walking at 5/6 of its usual speed, a train is 10 minutes too late. Find its usual time to cover the journey.

Solution:   New speed = 5/6 of the usual speed.

New time taken = 6/5 of the usual time.

So, (6/5 of the usual time) - (usual time) = 10 min.
=> 1/5 of the usual time = 10 min
=> usual time = 50 min.
9.
If a man walks at the rate of 5 kmph, he misses a train by 7 minutes. However, if he walks at the rate of 6 kmph, he reaches the station 5 minutes before the arrival of the train. Find the distance covered by him to reach the station.

Solution:   Let the required distance be x km.

Difference in the times taken at two speeds = 12 min = 1/5 hr.
x/5 - x/6 = 1/5
=> 6x - 5x = 6
=> x = 6.
Hence, the required distance is 6 km.
10.
A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?

Solution:   Suppose they meet x hours after 10 a.m.

Then, (Distance moved by first in x hrs) + [Distance moved by second in (x - 1) hrs] = 390.
65x + 35(x - 1) = 390
=> 100x = 425
=> x = 4   1/4

So, they meet 4 hrs. 15 min. after 10 a.m. i.e., at 2.15 p.m.
11.
A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.

Solution:   Let the speed of the goods train be x kmph.

Distance covered by goods train in 10 hours
= Distance covered by express train in 4 hours
10x = 4 * 90
=> x = 36.

So, the speed of goods train = 36 kmph.
12.
A thief is spotted by a policeman from a distance of 100 metres. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8 km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?

Solution:   Relative speed of the policeman = (10 - 8) km/hr = 2 km/hr.

Time taken by policeman to cover 100 m = [(100/1000) * (1/2)] hr = 1/20 hr.

In 1/20 hrs, the thief covers a distance of [8 * (1/20)] km = 2/5 km = 400 m.
13.
I walk a certain distance and ride back taking a total time of 37 minutes. I could walk both ways in 55 minutes. How long would it take me to ride both ways?

Solution:   Let the distance be x km.

Then, (Time taken to walk x km) + (Time taken to ride x km) = 37 min.
(Time taken to walk 2x km) + (Time taken to ride 2x km) = 74 min.
But, time taken to walk 2x km = 55 min.

Time taken to ride 2x km = (74 - 55) min = 19 min.
14.
A car moves at the speed of 80 km/hr. What is the speed of the car in metres per second? [Hotel Management 2002]