) A police van travelling at 60 kmph crosses an escaping thief
travelling in opposite direction at 48 kmph. The police van has to
travel for a further 5 minutes before it can find a gap in the
median where it can take a U tern and start chasing the thief.
After how much time police van catch the thief?

Question

Answer

Problem:

A police van travelling at 60 kmph crosses an escaping thief travelling in opposite direction at 48 kmph. The police van has to travel for a further 5 minutes before it can find a gap in the median where it can take a U tern and start chasing the thief. After how much time police van catch the thief? Explain in details.

Solution:

To find out how much time the police van will take to catch the thief, we need to follow the steps mentioned below:

Step 1: Calculate the distance between the police van and the thief

Let's assume that the distance between the police van and the thief at the time of their meeting is 'd'.

As they both are travelling in opposite directions, the relative speed between them will be the sum of their speeds, which is 60+48 = 108 kmph.

As they meet each other, the total distance covered by both of them will be equal to 'd'.

Hence, we can apply the formula: distance = speed x time.

So, d = 108 x t, where 't' is the time they took to meet each other.

Step 2: Calculate the time taken by the police van to turn around and start chasing the thief

As given in the problem, the police van takes 5 minutes to find a gap in the median and take a U-turn.

5 minutes is equal to 5/60 = 1/12 hours.

So, after the U-turn, the police van will start chasing the thief after 1/12 hours.

Step 3: Calculate the time taken by the police van to catch the thief

Let's assume that the time taken by the police van to catch the thief is 't1'.

After the U-turn, the police van and the thief will start moving towards each other.

So, the relative speed between them will be the difference between their speeds, which is 60-48 = 12 kmph.

As they meet each other, the total distance covered by both of them will be equal to 'd'.

Hence, we can apply the formula: distance = speed x time.

So, d = 12 x t1, where 't1' is the time taken by the police van to catch the thief.

Step 4: Calculate the total time taken by the police van to catch the thief

The total time taken by the police van to catch the thief will be the sum of the time taken by the police van to turn around and start chasing the thief, and the time taken by the police van to catch the thief.

So, the total time taken by the police van to catch the thief will be: t = t

Answer

Police van had to move for 5 mins before it could take a u turn

Distance travelled by police van before u-turn = (60*5/60)km = 5km

So, at the time of crossing police was 5 km behind u turn and thief was 5km ahead of u turn

Distance travelled by thief by the time police has reached the u - turn= (48*5/60)km= 4km

The police van has reached the u turn so, now the distance between police and thief is 9km

Now suppose starting from u turn, police caught the thief after t time

Then, distance travelled by police in t time = distance travelled by thief in t time + 9km

60*t = 48*t + 9
t = 3/4 hrs or 45 mins

So total time is (45+5) =50mins

Similar GATE Doubts

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A train that is 280 metres long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in metres?

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