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| Math Central | Quandaries & Queries |
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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. |
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,
Penny
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