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6 April, 13:55

On a trip, a motorist drove 150 miles in the morning and 50 miles in the afternoon. His average rate in the morning was twice his average rate in the afternoon. He spent 5 hours driving. Find his average rate on each part of the trip.

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  1. 6 April, 14:25
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    If three numbers have a ratio of 7:3:2, we can set up two equations from that:

    a/b = 7/3

    a/c = 7/2

    and if the sum of the smallest and largest is 30 more than twice the second:

    a + c = 2b + 30

    We now have three equations and three unknowns.

    I'll solve the first two equations for "a", then use them to create a new equation with two variables, and use one of them to change the third equation into a new equation with the same two variables:

    a/b = 7/3

    3a = 7b

    a = 7b/3

    a/c = 7/2

    2a = 7c

    a = 7c/2

    7b/3 = 7c/2

    14b = 21c

    2b = 3c < - - first new equation

    a + c = 2b + 30

    (7c/2) + c = 2b + 30

    7c + 2c = 4b + 60

    9c = 4b + 60 < - - second new equation

    Now that we have a new system of two equations and two unknowns, this is easilly solved.

    2b = 3c

    b = 3c/2

    9c = 4b + 60

    9c = 4 (3c/2) + 60

    9c = 6c + 60

    3c = 60

    c = 20

    Now that we have c, we can find a and b:

    a = 7c/2

    a = 7 (20) / 2

    a = 70

    a = 7b/3

    70 = 7b/3

    210 = 7b

    b = 30

    The solution is:

    70, 30, and 20
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