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3 January, 10:45

A snowstorm causes a bus driver to decrease the usual average rate a 180 mile route by 5 miles per hour. As a result, the bus takes three hours longer than usual to complete the route. At what average rate does the bus usually cover a 180 mile route?

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  1. 3 January, 10:59
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    180/v=t and 180 / (v-5) = 3+t using t from the first in the second ...

    180 / (v-5) = 3+180/v

    180 / (v-5) = (3v+180) / v cross multiplying ...

    180v = (3v+180) (v-5)

    180v=3v^2-15v+180v-900

    3v^2-15v-900=0

    v^2-5v-300=0

    v^2-20v+15v-300=0

    v (v-20) + 15 (v-20) = 0

    (v+15) (v-20) = 0, since v>0

    v=20mph

    So the bus usually travels at 20mph

    check ...

    normal ... 180/20=9 hours

    snow ... 180/15=12 hours

    correct.
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