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4 October, 05:54

Mike has one hour to spend at the gym where he will jog, play handball and cycle. jogging uses 10 calories per minute, handball uses 9 calories per minute and cycling uses 12 calories per minute. mike jogs as long as he cycles. how long should mike participate in each of these activities in order to use 580 calories? find the number of minutes needed for playing handball.

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  1. 4 October, 06:16
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    Let

    x = minutes used for jogging

    y = minutes used for handball

    z = minutes used for cycling

    Th total time spent is 1 hour (60 minutes), therefore

    x + y + z = 60

    Because Mike jogs as long as he cycles, therefore

    x = z

    Therefore

    2x + y = 60

    or

    y = 60 - 2x (1)

    Jogging consumes 10 calories/min, handball consumes 9 calories/min and cycling consumes 12 calories/min.

    The calories consumed in 60 minutes is 580, therefore

    10 x + 9y + 12z = 580

    Because x = z,

    22x + 9y = 580 (2)

    Substitute (1) into (2).

    22x + 9 (60 - 2x) = 580

    22x + 540 - 18x = 580

    4x = 40

    x = 10

    y = 60 - 2x = 40

    z = x = 10

    Answer:

    10 minutes of jogging

    40 minutes of handball

    10 minutes of cycling.
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