Answer: each of the workout plans lasts for 0.75 hours
Explanation:
Let x represent the amount of time that plan A lasts.
Let y represent the amount if time that plan B lasts.
On Wednesday there were 7 clients who did Plan A and 9 who did Plan B. Mary trained her Wednesday clients for a total of 12 hours. This means that
7x + 9y = 12 - - - - - - - - - - -1
On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Mary trained her Thursday clients for a total of 6 hours. This means that
5x + 3y = 6 - - - - - - - - - - - -2
Multiplying equation 1 by 5 and equation 2 by 7, it becomes.
35x + 45y = 60
35x + 21y = 42
Subtracting, it becomes
24y = 18
y = 18/24 = 0.75
Substituting y = 0.75 into into equation 1, it becomes
7x + 9 × 0.75 = 12
7x + 6.75 = 12
7x = 12 - 6.75 = 5.25
x = 5.25/7 = 0.75