Algebra

The boat travels 60 miles to an island and the same 60 miles coming back. Changes in the wind and tide made the average speed on the return trip 3 mph slower than the speed on the way out. If the total time of the trip took 9 hours, find the speed going to the island and the speed on the return trip.

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  1. return speed = v - 3

    time out = 60/v
    time back = 60/(v-3)
    so
    60/v + 60/(v-3) = 9
    60(v-3) + 60 v = 9 v(v-3)

    9 v^2 -27v = 120 v - 180

    9 v^2 - 147 v + 180 = 0
    3 v^2 - 49 v + 60 = 0
    (3 v -4)(v-15) = 0
    v = 15 or v = 4/3
    4/3 will not work because v - 3 is negative
    try v = 15
    15 and 15-3 = 12
    then
    60/v = 4
    60/12 = 5
    sure enough 9 hours

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