Math CentralQuandaries & Queries


Question from Jordan, a student:

Sammy owns a motorboat that travels 4 miles/hour in still water. It goes 12 miles upstream and 12 miles back again (downstream) in a total of 8 hours. Find the speed of the current of the river.

I'm having trouble setting up an equation to solve this. I usually use a table to set it up but not understanding this one.
Thanks for the help!

Hi Jordan,

Suppose the speed current is c miles per hour and it took Sammy t hours to go the 12 miles upstream. Going upstream his speed is (4 - c) miles per hour and hence

(4 - c) t = 12 miles.

Downstream his speed is (4 + c) and it takes him (8 - t) hours to go the 12 miles so

(4 + c) (8 - t) = 12 miles.

Solve the first equation for t, substitute into the second equation an solve for c.

Make sure you check your answer,

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