Brian the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 5 clients who did Plan A and 3 who did Plan B. On Tuesday there were 2 clients who did Plan A and 6 who did Plan B. Brian trained his Monday clients for a total of 10 hours and his Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
Let's say Plan A lasts x hours and Plan B lasts y hours.
From the information given, we can create the following system of equations:
5x + 3y = 10 (total hours trained on Monday)
2x + 6y = 10 (total hours trained on Tuesday)
Now, we can solve this system of equations to find the values of x and y.
From the first equation, we can rearrange it to solve for x:
5x = 10 - 3y
x = (10 - 3y) / 5
x = 2 - (3/5)y
Now, we can substitute this expression for x into the second equation:
2(2 - (3/5)y) + 6y = 10
4 - 6/5y + 6y = 10
-6/5y + 6y = 6
-6y + 30y = 30
24y = 30
y = 30/24
y = 5/4
y = 1.25
Now that we have the value of y, we can substitute it back into the expression for x:
x = 2 - (3/5)(1.25)
x = 2 - 0.75
x = 1.25
Therefore, Plan A lasts for 1.25 hours and Plan B lasts for 1.25 hours.