Question

Hans 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 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Hans trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?

Answer 1

A = hours for plan A
B = hours for plan B

Monday: 6A + 5B = 7
Tuesday: 2A + 3B = 3

use elimination by multiplying the 2nd equation by 3.

Doing that we get 3(2A + 3B = 3) = 6A + 9B = 9

So the two equations are now:
6A + 9B = 9

6A + 5B = 7

Subtract and we have 4B = 2

B = 2/4 = 1/2 of an hour

Now put 1/2 back into either equation to solve for A

6A + 5(1/2) = 7
6A + 5/2 = 7
6A = 14/2 -5/2
6A = 9/2
divide by 6 to get A = 9/12 = ¾ hours

Plan A = 3/4 hour

Plan B = 1/2 hour