Joel has one hour to spend at the gym where he will jog, play handball and cycle. jogging uses 13 calories per minute, handball uses 11 calories per minute and cycling uses 14 calories per minute. joel jogs as long as he cycles. how long should joel participate in each of these activities in order to use 700 calories? find the number of minutes for playing handball.

Handball = 44 minutes Cycling = 8 minutes Jogging = 8 minutes Let's use the following variables j = Time Joel jogs. h = Time Joel plays handball c = Time Joel cycles. Now make some expressions to describe the problem. 13j + 11h + 14c = 700 j=c h = 60 - j - c Now substitute c for j in the expressions. 13c + 11h + 14c = 700 h = 60 - c - c = 60 - 2c Now substitute 60 - 2c for h 13c + 11(60 - 2c) + 14c = 700 And solve for c 13c + 11(60 - 2c) + 14c = 700 13c + 660 - 22c + 14c = 700 13c - 22c + 14c = 40 5c = 40 c = 8 So we now know the 8 minutes were spent cycling. And because of j=c, we also know that 8 minutes were spent jogging. And finally, because of h=60-2c, we know that 44 minutes were spent playing handball.