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| Math Central | Quandaries & Queries |
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Question from Kathleen, a student: It took a boat 2 hours to reach town A going upstream. The way back was 1h20 min. What is the speed of the boat in still water if the speed of the stream is 3 mph? |
Hi Kathleen,
There are two trips, one upstream and the other downstream and on each trip
\[\mbox{ rate } = \frac{\mbox{distance}}{\mbox{time}}\]
where the rate is the speed of the boat in the moving water.
Let $d$ miles be the distance the boat travels upstream. Suppose the rate of the boat in still water is $s$ mph then, since the water is flowing at 3 mph the rate at which the boat travels upstream is $s - 3$ mph. Write the equation
\[\mbox{ rate } = \frac{\mbox{distance}}{\mbox{time}}\]
for the trip upstream.
On the trip downstream what is the speed of the boat in the moving water? Write the equation for the rate on the trip downstream. Solve the two equations for $s.$
Penny
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