First define your variables. I will use the following:
x = Minutes on stationary bike
y = Minutes on stair climber
Next, we need to find 2 equations that relate the two variables.
Since the total number of minutes in the workout is 60, the number of minutes on the stationary bike (x) plus the number of minutes on the stair climber (y) add up to 60:
x + y = 60
Since the number of calaries burned on the stationary bike (9 calaries per minute X x minutes) plus the number of calaries burned on teh stair climber (11 calaries per minute X y minutes) adds up to the total number of calaries (590):
9x + 11y = 590
Now that we have two equations, we can solve for one of the variables using either substitition or elemination method. I am going to use elimination.
I will begin by multiplying the first equation by -9 and adding the second equation.
-9x - 9y = -540
+9x +11y = 590
0 + 2y = 50
2y = 50
y = 25
By substituting the value of y I found into the first equation, we get:
x + 25 = 60
x = 35
Therefore, the athlete would spend 35 minutes on the stationary bike and 25 minutes on the stair climber.