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| Math Central | Quandaries & Queries |
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Question from Fran, a student: Kim paddled a canoe 10 km upstream and then paddled back to his starting point. If the rate of the current was 2 km/h that day and the whole trip took 3.75 h, how fast does Kim paddle in still water? Olivia drove x km at 60 km/h and then twice as far at 80 km/h. In terms of x, how many hours did the trip take? |
Hi Fran,
The key to both of these problems is the units. In both instances the rate is in km/hr so
rate = distance/time (1)
For Kim's problem suppose that the rate she travels in still water is r km/hr. Thus paddling upstream her rate is (r - 2) km/h and on the return trip her rate is (r + 2) km/h. Use equation (1) to write an expression for the time for each of the two legs of the trip and then add these times to get 3.75 h. Solve for r.
Use equation 1 to find an expression for the time it took Olivia to drive x km at 60 km/h?
Use equation 1 to find an expression for the time it took Olivia to drive 2x km at 80 km/h?
I hope this helps,
Penny
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