Algebra

A passenger boat which travels 6 mph faster than a freighter required 3 days less time to make a trip of 2592 miles. Find the rate of the passenger boat.

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asked by Lina
  1. rate of passenger boat --- x mph
    rate of freighter --------- x-6 mph

    2592/(x-6) - 2592/x = 72 , assuming they travel 24 hours per day

    multiply each term by x(x-6)

    2592x - 2592(x-6) = 72x(x-6)
    2592x - 2592x + 15552 = 72x^2 - 432x

    72x^2 - 432x - 15552 = 0
    9x^2 - 54x - 1944= 0
    (x - 18)(9x + 108) = 0
    x = 18 or x is a negative

    the rate of the passenger boat was 18 mph
    the rate of the freighter was 12 mph

    check
    2592/18 = 144 hrs
    2592/12 = 216441 hrs
    difference is 216-144 = 72
    My answer of x = 18 is correct

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    posted by Reiny

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