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24 October, 09:38

It takes 36 minutes less time to travel 120 miles by car at night than by day because the lack of traffic allows the average speed at night to be 10 miles per hour faster than the daytime. Find the average speed in the daytime.

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  1. 24 October, 10:10
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    Let the average speed at day time be x miles per hour

    Therefore at night the average speed = (x + 10) miles per hour

    Time = Distance / speed

    Time at day - Time at night = 36 minutes.

    36 minutes = 36/60 hour = 6/10 hour

    Time at day = Distance / speed at day = 120 / x

    Time at night = Distance / speed at night = 120 / (x + 10)

    120/x - 120 / (x + 10) = 6/10

    1/x - 1 / (x + 10) = 6/10 * 1/120

    1/x - 1 / (x + 10) = 1/200

    ((x + 10) - x) / ((x) (x+10)) = 1/200

    (x + 10 - x) / ((x) * (x+10)) = 1/200

    10 / ((x) * (x + 10)) = 1/200

    1 / ((x) * (x + 10)) = 1/2000

    Therefore x (x + 10) = 2000

    x and x + 10 are 40 and 50. Because 40*50 = 2000

    x = 40

    Average speed in the day time = 40 miles per hour
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