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19 March, 22:00

You ride your bike x miles per hour up a mountain for 45 minutes. On the way down the mountain, you ride your bike 2 miles per hour faster. It takes 20 minutes to ride your bike down the mountain. How far did you ride your bike in total?

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  1. 20 March, 01:38
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    2 2/5 (or 2.4) miles.

    Step-by-step explanation:

    Your speed up the mountain =

    x = distance / time = d / 3/4 where d is the distance travelled up the mountain. (its 3/4 because 45 minutes = 3/4 hour).

    Coming down the mountain your speed

    = x + 2 = d / 1/3 (the distance is also d travelling down).

    Simplifying the 2 equations:

    x = 4d/3

    x + 2 = 3d

    Substituting x = 4d/3 in the fist equation>

    4d/3 + 2 = 3d

    Multiply through by 3

    4d + 6 = 9d

    6 = 5d

    d = 6/5 miles.

    The total distance you rode = 2 * 6/5

    = 12/5

    = 2 2/5 miles.
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