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20 April, 01:41

Greg 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 Wednesday there were 3 clients who did Plan A and 5 who did Plan B. On Thursday there were 9 clients who did Plan A and 7 who did Plan B. Greg trained his Wednesday clients for a total of 6 hours and his Thursday clients for a total of 12 hours. How long does each of the workout plans last?

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  1. 20 April, 01:57
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    This problem can be solved by algebraic method.

    Let

    x = the total time spent of all clients in Plan A

    y = the total time spent of all clients in Plan B

    We represent two variables x and y because there are two plans that won't be happened simultaneously.

    On Wednesday, the two workout plans have the total time of 6 hours. We equate

    3x + 5y = 6

    While on Thursday, the total time is 12 hours. We also equate

    9x + 7y = 12

    To find x and y, we can use the substitution method. For the first equation, we arrange it in terms of y, that is

    5y = 6 - 3x

    y = (6 - 3x) / 5

    Substitute it to the second equation:

    9x + (7/5) (6 - 3x) = 12

    9x + (42/5) - (21/5) x = 12

    Multiply the equation by 5 to cancel the denominator:

    45x + 42 - 21x = 60

    45x - 21x = 60 - 42

    24x = 18

    x = 18/24 = 3/4 hours

    For y:

    3 (3/4) + 5y = 6

    9/4 + 5y = 6

    Multiply the equation by 4 to cancel the denominator:

    9 + 20y = 24

    20y = 24 - 9

    20y = 15

    y = 15/20 = 3/4 hours

    Hence, each workout plans are done within 3/4 hours (or 45 minutes).
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