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

Question

A) Assuming a constant paddling effort throughout, how fast is the river flowing?
B) What would the canoe speed in a still lake be for the same paddling effort?

Two students are canoeing on a river. while heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1.8 h , reaching a point 2.1 km 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) 5.6 km downstream from the turn-around point.

Explanation / Answer

C is the speed of canoe , R is the speed of river

Paddling for 1.8 hour, reaching a point 2.1km farther upstream

=> C - R = 2.1/1.8 km/h

=> C = 1.16 + R

t = D / R , the bottle has 1.8 hour head start

=> 5.6 / (C + R) = (3.5 / R) - 1.8

=> 5.6 / (C + R) = (3.5 - 1.8*R) / R

=> 5.6R = 3.5C - 1.8C*R + 3.5R - 1.8R^2

Substituting

=>5.6R = 3.5(1.16 + R) - 1.8R(1.16+ R) + 3.5R - 1.8R^2

=> 5.6R = 4.06 + 3.5R - 2.08R - 1.8R^2 + 3.5R - 1.8R^2
=> 0 = 3.6R^2 - 0.68R - 4.06

R = 1.16 km/h

C = 1.16+1.16= 2.32 km/h

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