# Having trouble with this canoe/relative velocity problem.

## Homework Statement

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1.5 h, reaching a point 1.1 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) 4.1 Km downstream from the turn-around point.

## The Attempt at a Solution

I got the speed in the first phase of the problem, (1.1km/1.5h) but don't know where to go from here.

Thanks!

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Spinnor
Gold Member

## Homework Statement

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1.5 h, reaching a point 1.1 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) 4.1 Km downstream from the turn-around point.

## The Attempt at a Solution

I got the speed in the first phase of the problem, (1.1km/1.5h) but don't know where to go from here.

Thanks!
I think it helps to draw a picture. I did and came up with three equations in three unknowns:

(1.5 + t)*S_r = 3km
t*(S_r + S_b) = 4.1km
(S_b - S_r)*1.5 = 1.1km

(1.5hr + t) is the total time of the trip, S_r is the speed of the river, and S_b is the speed of the boat in still water.

Ugh. I kept coming up with 2 equations with 3 unknowns... thank you so much.

I went to thread tools, but there isn't an option to mark the question solved...