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Math Help - Algebra question help needed

  1. #1
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    Post Algebra question help needed

    At this year's marathon, Fred took 3 hours to cover the 42km distance.
    At next year's marathon, Fred wants to improve his net time by six minutes. He will try a different strategy of running for the first two hours at a certain speed (x), and then completing the rest of the race at a rate 2km per hour faster than his speed this year which was 14km per hour. If he is to succeed, at what speed will he need to run for the first two hours of next year's marathon?


    what I have worked out so far:
    The speed at which Fred completes the rest of the race is 16km per hour (14km + 2km = 16km/hour).
    3 hours minus 6 minutes = 2 hours 54 minutes. This is how long his race should take next year.
    After he has covered the first two hours, Fred will have 54 minutes left. This means he won't cover 16km since 54min is not a whole hour, however he should cover 8km every half hour.

    What I need help with is:
    working out what x =
    Is 2 hours and 54 minutes the correct time Fred's race should take next year?

    thanks to everyone who points me in the right direction.
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  2. #2
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    Re: Algebra question help needed

    You are on the correct line.
    assume the sped during the first two hours next year to be x kpm the remaining time is 54 m.
    thus total distance is 2 * x + 16 * ( 54 / 60 ) = 2x + 14.4 = 42 [ the given distance ]
    That gives x = 13.8
    Know you can conclude
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