Question

Ryan 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 Wednesday there were 5

clients who did Plan A and 3 who did Plan B. On Thursday there were 2 clients who did Plan A and 6 who did Plan B. Ryan trained his Wednesday clients for a total of 10
hours and his Thursday clients for a total of 10 hours. How long does each of the workout plans last?

Answer 1

Both plans last for 1.25 hours (1 hour 15 minutes)

Explanation:

Let x hours be the time needed for plan A and y hours be the time needed for plan B.

On Wednesday there were 5 clients who did Plan A and 3 who did Plan B. Thus, 5x+3y=10.

On Thursday there were 2 clients who did Plan A and 6 who did Plan B. Thus, 2x+6y=10.

Solve the sytem of two equation. Multiply the first equation by 2, the second by 5 and subtract them:

`10x+6y-10x-30y=20-50,\\ \\-24y=-30,\\ \\y=(30)/(24)=(5)/(4)=1.25\ hours.`

Therefore,

`5x+3\cdot 1.25=10,\\ \\5x=10-3.75=6.25,\\ \\x=1.25\ hours.`