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3 January, 02:50

Byron wanted to try out different watercraft. He went 124 miles downstream in a motorboat and 45 miles downstream on a jet ski. His speed on the jet ski was 10 mph faster than in the motorboat. Byron spent a total of 4 hours on the water. What was his rate of speed, in miles per hour, in the motorboat?

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  1. 3 January, 05:02
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    the speed of the motorboat was 90.313 mph

    Explanation:

    since the distance d covered for each watercraft is

    d = v*t, where v = velocity and t = time spent in that watercraft

    the difference in speed will be

    v₂-v₁ = d₂/t₂ - d₁/t₁ = 10 mph

    with the constraint

    t₂ + t₁ = 4 hours → t₂ = 4 - t₁

    where 2 represents motorboat and 1 jet ski

    then

    d₂/t₂ - d₁/t₁ = 10

    d₂ / (4 - t₁) - d₁/t₁ = 10

    d₂*t₁ - d₁ * (4 - t₁) = 10 * t₁ * (4 - t₁)

    d₂*t₁ - 4*d₁ + d₁*t₁ = 40*t₁ - 10*t₁²

    10*t₁² + (d₂+d₁-40) * t₁ - 4*d₁ = 0

    replacing values of distances

    10*t₁² + (d₂+d₁-40) * t₁ - 4*d₁ = 0

    10*t₁² + (45+124 - 40) * t₁ - 4*124 = 0

    10*t₁² + 129 * t₁ - 496 = 0

    then

    t₁ = [-129 + √ (129²+4*10*496) ] / (2*10) = 1.373 hours

    therefore

    v₁ = d₁/t₁ = 124 miles/1.373 hours = 90.313 mph

    thus the speed of the motorboat was 90.313 mph
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