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12 October, 05:09

Hans the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Hans trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?

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  1. 12 October, 05:33
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    A = hours for plan A

    B = hours for plan B

    Monday: 6A + 5B = 7

    Tuesday: 2A + 3B = 3

    use elimination by multiplying the 2nd equation by 3.

    Doing that we get 3 (2A + 3B = 3) = 6A + 9B = 9

    So the two equations are now:

    6A + 9B = 9

    6A + 5B = 7

    Subtract and we have 4B = 2

    B = 2/4 = 1/2 of an hour

    Now put 1/2 back into either equation to solve for A

    6A + 5 (1/2) = 7

    6A + 5/2 = 7

    6A = 14/2 - 5/2

    6A = 9/2

    divide by 6 to get A = 9/12 = ¾ hours

    Plan A = 3/4 hour

    Plan B = 1/2 hour
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