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Phrases Boat And Stream PYQ

Phrases PYQ
A motorboat going downstream passes a raft at point A. Exactly one hour later it turned back and while coming upstream it passed the same raft at point B, 6 km from point A. What is the speed of the water current in km/hr?





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Phrases Previous Year PYQ Phrases NIMCET 2009 PYQ

Solution

Let:
Boat speed in still water = v
Current speed = c

Downstream speed = v + c
Upstream speed = v – c

Key observation:
In 1 hour, the raft (moving with the current) travels c × 1 = c km from A.

Distance between A and B = 6 km
So during the entire boat cycle, the raft moved 6 km purely due to current.

Time taken by boat after passing raft until it meets again:
Downstream for 1 hour + Upstream time (t)
Raft moves 6 km in this total time:

c × (1 + t) = 6 … (i)

Distance boat travels upstream:
(v + c) × 1 = (v – c) × t + 6

But using standard result of this classic problem:
Current speed = distance / 2
= 6 / 2
= 3 km/hr

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