college algebra

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Solve the problem. A man rode a bicycle for 12 miles and then hiked an additional 8 miles. The total time for the trip was 5 hours. If his rate when he was riding a bicycle was 10 miles per hour faster than his rate walking, what was each rate?

  • college algebra -

    let walking rate be x mph
    let biking rate be x+10

    time for walking = 12/x
    time biking = 8/(x+10)

    isn't 12/x + 8(x+10) = 5 ?

    multiply each term by x(x+10)
    you will get quadratic, solve for x

  • college algebra -

    Let the walking speed be v and the bike speed V = v + 10.
    12/(v+10) + 8/v = 5 is the sum of the times spent bidking and walking.

    Solve that equation for v. You will have to start with a common denominator.
    [12v + 8(v+10)]/[v(v+10)] = 5
    5 v^2 + 50 v = 20 v + 80
    v^2 + 6v - 16 = 0
    (v + 8)(v -2) = 0
    Choose the positive root, v = 2 miles/hr
    The bike speed was then v + 10 = 12 mph.

  • college algebra -

    go with drwls solution, I mixed up the two rates.

  • college algebra -

    Solve. V^2-6v-16=0

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