Joe the trainer has two solo work out plans That he offers his clients. Plan A and Plan B. Each client does either one or the other (not both). On Friday there were 3 clients who did plan A and 2 who did Plan B. On Saturday there were 5 clients who did plan A and 6 who did plan B. Joe trained his friday clients for a total of 3 hours and his saturday clients for a total of 7 hours. How long does each workout plan last.

plan A lasts for 0.5 hour. Plan B lasts for 0.75 hour.

Step-by-step explanation:

Let x represent the duration of plan A.

Let y represent the duration of plan B.

On Friday there were 3 clients who did plan A and 2 who did Plan B.

Joe trained his Friday clients for a total of 3. It means that

3x + 2y = 3- - - - - - - - - -1

On Saturday there were 5 clients who did plan A and 6 who did plan B. Joe trained his Saturday clients for a total of 7 hours. It means that

5x + 6y = 7- - - - - - - - - 2

Multiplying equation 1 by 5 and equation 2 by 3, it becomes

15x + 10y = 15

15x + 18y = 21

Subtracting, it becomes

- 8y = - 6

y = - 6/-8

y = 0.75

Substituting y = 0.75 into equation 1, it becomes

3x + 2 × 0.75 = 3

3x + 1.5 = 3

3x = 3 - 1.5 = 1.5

x = 1.5/3

x = 0.5