Question

Keisha the trainer has two solo workout plans that she offers her 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 5 who did Plan B. On Saturday there were 12 clients who did Plan A and 2 who did Plan B. Keisha trained her Friday clients for a total of 9 hours and her Saturday clients for a total of 9 hours. How long does each of the workout plans last?

Answer 1

Plan A lasts 0.5 minutes

Plan B lasts 1.5 hours

Explanation:

Let Plan A last
`a` hours, and Plan B last
`b` hours.

We have

`\left \{ {{3a+5b=9} \atop {12a+2b=9}} \right.`

We'll multiply the top equation by 4, then subtract the second equation from it to get

`18b=27\\b=1.5`

We'll substitute this back into the original first equation
`3a+5b=9` to get

`3a+7.5=9\\3a=1.5\\a=0.5`

`\therefore \left \{ {{a=0.5} \atop {b=1.5}} \right.`