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. Answer:    16 miles

    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.
    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


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