Question

A fisherman can row upstream at 2 mph and downstream at 8 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. How far
did the fisherman row if the entire trip took 5 hours?

1. thienan

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Explanation:
x = time in hours spent going upstream
5-x = remaining time in hours spent going downstream
Those two quantities add to 5 hours total.
Let’s find the expression for how far the fisherman went upstream
distance = rate*time
d = r*t
d = 2x
Do the same for the downstream portion
d = r*t
d = 8(5-x)
d = 40-8x
The values of d refer to the same distance because he came back to the starting point.
Set those right hand sides equal to one another and solve for x.
2x = 40-8x
2x+8x = 40
10x = 40
x = 40/10
x = 4
5-x = 5-4 = 1
He spent 4 hours going upstream, and the remaining 1 hour coming back downstream.
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If he spent 4 hours going upstream at 2 mph, then he traveled d = r*t = 2*4 = 8 miles.
The remaining 1 hour going downstream at 8 mph means he traveled d = r*t = 8*1 = 8 miles, which matches with the previous result. This confirms we have the correct one-way distance of 8 miles.
Therefore, the total round trip distance is 2*8 = 16 miles