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.

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

10 minutes of jogging
40 minutes of handball
10 minutes of cycling.

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