CAT Practice : Speed Time, Races

If you go upstream the stream is against you, if you travel downstream, the stream aids you. What if you want to cross over to the other side and drive perpendicular to the stream?

Boats and Streams

Q.10: City A to City B is a downstream journey on a stream which flows at a speed of 5km/hr. Boats P and Q run a shuttle service between the two cities that are 300 kms apart. Boat P, which starts from City A has a still-water speed of 25km/hr, while boat Q, which starts from city B at the same time has a still-water speed of 15km/hr. When will the two boats meet for the first time? (this part is easy) When and where will they meet for the second time?
1. 7.5 hours and 15 hours
2. 7.5 hours and 18 hours
3. 8 hours and 18 hours
4. 7.5 hours and 20 hours

Choice D. 7.5 hours and 20 hours

Detailed Solution

When boat P travels downstream, it will effectively have a speed to 30kmph. Likewise, Q will have an effective speed of 10kmph. The relative speed = 40kmph. So, the two boats will meet for the first time after ${300 \over 40}$ hours (Distance/relative speed) = 7.5 hours (Actually, for this part we do not need the speed of the stream)

The second part is more interesting, because the speed of the boats change when they change direction. Boat P is quicker, so it will reach the destination sooner. Boat P will reach City B in 10 hours ${300 \over 30}$. When boat P reaches city B, boat Q will be at a point 100kms from city B.

After 10 hours, both P and Q will be travelling upstream,
P's speed = 20 km/hr
Q's speed = 10 km/hr
Relative speed = 10km/hr
Q is ahead of P by 100 kms

P will catch up with Q after 10 more hours ${{Distance \over Relative Speed} {-} {100 \over 10}}$.

So, P and Q will meet after 20 hours at a point 200 kms from city B.

Correct Answer: 7.5 hours and 20 hours

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"Life is a race ... if you don't run fast ... you will be like a broken undaa" - Veerusahasra Buddhi