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21 votes
21 votes
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?

User DWal
by
3.0k points

1 Answer

7 votes
7 votes

Answer: 16 miles

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Step-by-step 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

User Yomi
by
3.0k points