Question

Brittany uses the ski machine and the treadmill at the gym for an exercise program. Her trainer wants her on an exercise program that meets these two conditions:

1) Brittany will exercise for at least 45 minutes and at most 1 hour and 15 minutes,
dividing her time between the ski machine and the treadmill.
2) Brittany will spend at least three times as much time on the treadmill as on the
ski machine.
a. Let x represent the time on the ski machine and y represent the time on the
treadmill. Write a system of inequalities that models the relationships between the
amounts of time Brittany spends on the two machines. You will have three
inequalities.

Answer 1

`x + y = 5 \\ 5 * 5 = 25`

Answer 2

Required inequalities are as following.

Brittany will exercise for at least 45 minutes:

• x + y ≥ 45

Brittany will exercise at most 1 hour and 15 minutes (= 75 min):

• x + y ≤ 75

Brittany will spend at least three times as much time on the treadmill as on the ski machine:

• y ≥ 3x