Math CentralQuandaries & Queries


Question from Jessica, a student:

The speed of the current in a river is 2mph. Jessica travels 20 miles upstream and then 20 miles downstream in a total time of 5 1/3 hr. Find the speed of the boat. I know you have to use V= d/t, but what is the equation for time because you have to factor in that upstream the boat is slower and downstream the boat is faster?
Hi Jessica,

Suppose that the speed of the boat is still water is b miles per hour. Thus going upstream her speed is b - 2 miles per hour and hence the time it takes to travel upstream 20 miles is given by time upstream = 20/(b - 2) hours.

Find the time it takes her to travel 20 miles downstream and add the two times to obtain the total time of 5 1/3 hours. This is an equation in b. Solve for b.

I hope this helps,
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