Question

Debra 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 Wednesday there were 5 clients who did plan A and 3 who did plan B. On Thursday there were 7 clients who did plan A and 9 who did plan B. Debra trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?

Answer 1

The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .

According to the question the plan only ran on wednesday and thursday.

Wednesday = plan A has 5 client and plan B has 3 clients.

Thursday = plan A has 7 client and plan B has 9 clients.

On wednesday she trained her client for 6 hours.

On thursday she trained her client for 12 hours.

let

x = hour of plan A workout for each client

y = hour of plan B workout for each client

`\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }(6)/(3)\text{ - }(5)/(3)x \\ y\text{ = 2 - }(5)/(3)x \\ 7x\text{ + 9(2 - }(5)/(3)x\text{) = 12} \\ 7x\text{ + 18 - }(45)/(3)x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }(6)/(8) \\ x\text{ = }(3)/(4) \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5((3)/(4))\text{ + 3y = 6} \\ (15)/(4)\text{ + 3y = 6} \\ 3y\text{ = 6 - }(15)/(4) \\ 3y\text{ = }(24-15)/(4) \\ 3y\text{ = }(9)/(4) \\ y\text{ = }(9)/(4)\text{ }*\text{ }(1)/(3) \\ y\text{ = }(9)/(12) \\ y\text{ = }(3)/(4) \end{gathered}`

on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs

On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs

Each of the work out lasted for 3/4 hrs = 0.75 hrs