Math CentralQuandaries & Queries


Question from Jenn, a student:

On the Amazon River in Brazil, a boat goes 50 miles upstream in 3 hours, later the boat returns to the starting point in 2 hours. What is the speed of the boat in still water and what is the current speed in this part of the Amazon?

Hi Jenn,

I can get you started.

The important concept here is that rate = distance/time. In the units you are using the rate (speed) is then in miles per hour.

Suppose that the speed of the boat in still water is s miles per hour and the speed of the river is r miles per hour. When the boat goes upstream it is going against the current so its speed is s - r miles per hour. Since the distance is 50 miles and going upstream took 3 hours you have

s - r = 50/3.

Find the analogous equation for the trip downstream and then solve the pair of equations for s and r.


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