Two students are canoeing on a river. While heading upstream, they accidentally

Question

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1.9h , reaching a point 1.3km farther upstream. At this point they realize that the bottle is missing and, driven by ecological awareness, they turn around and head downstream. They catch up with and retrieve the bottle (which has been moving along with the current) 5.6km downstream from the turn-around point.

Assuming a constant paddling effort throughout, how fast is the river flowing?

What would the canoe speed in a still lake be for the same paddling effort?

Explanation / Answer

c is the canoe , r is the river
paddling for 1.3 hour, reaching a point 1km farther upstream

c - r = 0.77 km/h

c = 0.77 + r
t = d / r ,

the bottle has 1.3 hour head start

5 / (c + r) = (4 / r) - 1.3

5 = (0.77+r + r) * (4 - 1.3r) / r

r = 1.53 speed of water or river

c = 0.77+1.53 = 2.30 = speed of canoe

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