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 1.1h , reaching a point 2.6km 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) 5.8km downstream from the turn-around point.

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?

Explanation / Answer

a) distance covered by bottle d1 = 5.8 -2.6 = 3.2km

time t = 1.1h

speed of current Vr = d1/t = 3.2/1.1 =2.91km/h

b) distance covered boat = 2.6 km

speed of boat with respect to ground upstream Vg = 2.6/1.1 = 2.36 km/h

if speed of boat in still water is Vb

Vg = Vb -Vr

Vb =Vg +Vr = 2.36 +2.91 =5.27km/h

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