The question says that "A canoeist paddled upstream for 2 hours, then downstream for 3 hours. The rate of the current was 2mph. When she stopped, the canoeist realised she was 20 miles downstream from her starting point. How many hours will it take her to paddle back to her starting point?"
My answer:
Let x be the rate in still water.
Rate upstream = (x-2).
Rate downstream = (x+2).
3(x+2)+2(x-2) = 20
x=18/5.
time = distance / rate
time = 20 / ((18/5)-2)
time = 12.5 hours
However the answer says that this is wrong and it's because (3x+6)+(2x-4) = 20 should've been (3x+6)-(2x-4) = 20. I don't understand why I should be subtracting the upstream rate from the downstream rate.
Best Answer
The reason you should subtract the upstream rate from the downstream rate is because she is going the opposite direction when she is travelling downstream from when she is going upstream, and the downstream direction is treated as positive in this problem.