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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Alvarado

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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Parker Blake · Answer 1

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.