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Algebra

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A boy can row a boat at a constant rate of 5 mi/hr in still water. He rows upstream for 19 minutes and then rows downstream, returning to his starting point in another 13 minutes. What is the rate of the current? What is the total distance traveled?

  • Algebra -

    let the speed of the current be x mph
    so rate upstream = 5-x mph
    and rate downstream = 5+x mph

    then
    19/60 (5-x) = 13/60 (5+x)
    19(5-x) = 13(5+x)
    95 - 19x = 65 + 13x
    30 = 32x
    x = 30/32 mph or .9375 mph
    total distance = 13/60(5.9375) = 1.296 miles each way.

    check:
    rate against current = 4.0625
    rate with the current = 5.9375

    time against current = 1.296/4.0625 = .316 hrs = 19.4 minutes
    time with current = 1.296/5.9375 = .2183 = 13.1 minutes
    (Acceptable round-off error)

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