A thief escapes from city A at 2 pm and flees towards city B at 40 kmp

Question

A thief escapes from city A at 2 pm and flees towards city B at 40 kmph. At 3 pm, the police realize the escape and start chasing the thief at 50 kmph. Simultaneously, a police team from station B also starts towards city A to apprehend the thief at a speed of 60 kmph. What should be the distance between A and B such that both the police team nab the thief at the same time?

1. 200 km
2. 240 km
3. 400 km
4. 440 km
5. 480 km

1. 200 km 
2. 240 km 
3. 400 km 
4. 440 km
5. 480 km

Shahalikhan · Answer

can be solved easily using relative velocity of basic physics

by 3pm theif travelled 40 kilometres.=1 hour * 40kmph

time of meet =distance/relative velocity

now thief and police will meet after 40/10=4 hours

10 because both police and theif travel in same direction.so relative velocity is 50-40.

police from b meet thief at the same 4 hours.relative velocity*4=distance between 40km point & city b

here as both travels in opposite direction relative velocity=40-(-60)=100kmph

so distance between 40km point & city b=4*100=400km

total distance =40+400=440

give kudos

verydisco · Answer

Here's how I solved it. By the time it's 3 PM, the thief has already traveled 40 kilometres. This means that the distance between the police and the thief at 3 PM is 40 kilometres from A.

The ratios of speeds of Police (A) to (Police B) to Police (C) is 5:6:4, which is also the ratio of the distances traveled since they're all travelling for the same amount of time till they meet. Now, using the ratios above, 5K-4K=40, which means K = 40.

So distances traveled by Police (A) and (B) are 200 and 240 kms respectively. Since they meet, we can add up these distances to find the distance between A and B which is 440 kms.

HouseStark · Answer

Here is my approach to this question,

thief started moving/fleeing from A to B in 1 hr early with respect to both the police teams.
the distance covered in 1 hr by the thief=1*40=40km

Now, both the cop started their journey from opposite directions but the time of their meet will be the same.

\frac{x}{50}=\frac{x-40}{40}

x=200km

t=\frac{200}{50}=4hr

the police who is travelling from B travels = 60*4=240km

now add both the distances=  240+200=440km

A thief escapes from city A at 2 pm and flees towards city B at 40 kmp

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