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Math Help - Physics homework... question

  1. #1
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    Physics homework... question

    Hi.

    I have a little problem with this question. I did the first two (a) and (b), hopefully I did it ok.

    I don't know how to do (c)... if anyone can help I'll be thankful.
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  2. #2
    MHF Contributor
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    Quote Originally Posted by Phoebe83 View Post
    Hi.

    I have a little problem with this question. I did the first two (a) and (b), hopefully I did it ok.

    I don't know how to do (c)... if anyone can help I'll be thankful.
    A nice exercise on Distance = rate*time
    Or distance = (average speed)(time)

    -------------------------
    a) Half the time at 35 mph, and half the time at 55 mph.
    Let D = distance from San Antonio to Houston, in miles.
    And T = total time of travel from San Antonio to Houston.

    distance = rate*time
    35(T/2) +55(T/2) = D
    Multiply both sides by 2,
    35T +55T = 2D
    90T = 2D
    Since average speed is D/T, then,
    Divide both sides by T,
    90 = 2D/T
    D/T = 90/2 = 45 mph --------------answer.

    ------------------------------
    b) Half the distance at 35 mph, and half the distance at 55 mph.

    time = distance/rate
    (D/2)/35 +(D/2)/55 = T
    D/70 +D/110 = T
    Multiply both sides by 70*110,
    110D +70D = 70*110*T
    180D = 7700T
    D/T = 7700/180 = 42.7777...mph, average speed -------answer.

    --------------------------
    c) The average speed for the whole trip.

    total time = distance/(ave. speed)
    a) T1 = D/45 hrs
    b) T2 = D/42.7777.... hrs
    So, average speed for a) and b) is
    = 2D/(T1 +T2)
    = 2D/(D/45 +D/42.7777...)
    = 2[(45)(42.7777..)] / [42.7777... +45]
    = 43.86 mph ----------------------------answer.
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