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22 June, 00:33

Fiora starts riding her bike at 20 mi/h. After a while, she slows down to 14 mi/h, and maintains that speed for the rest of the trip. The whole trip of 112 miles takes her 6.5 hours. For how long did she travel at 20 mi/h?

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  1. 22 June, 03:12
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    3.5 hours

    Explanation:

    Speed = distance/time

    Let the distance that Fiora biked at 20 mi/h through be x miles and the time it took her to bike through that distance be t hours at 20 mi/h

    Then, the rest of the distance that she biked at 14 mi/h is (112 - x) miles

    And the time she spent biking at 14 mi/h the rest of the distance = (6.5 - t) hours

    Her first biking speed = 20 mph = 20 miles/hour

    Speed = distance/time

    20 = x/t

    x = 20 t (eqn 1)

    Her second biking speed = 14 mph = 14 miles/hour

    14 = (112 - x) / (6.5 - t)

    112 - x = 14 (6.5 - t)

    112 - x = 91 - 14t (eqn 2)

    Substitute for x in (eqn 2)

    112 - 20t = 91 - 14t

    20t - 14t = 112 - 91

    6t = 21

    t = 3.5 hours

    x = 20t = 20 * 3.5 = 70 miles.

    (112 - x) = 112 - 70 = 42 miles

    (6.5 - t) = 6.5 - 3.5 = 3 hours

    Meaning that she travelled at 20 mi/h for 3.5 hours.
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