Question

Miguel 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 2 who did Plan B. On Tuesday there were 3 clients who did Plan A and 8 who did Plan B. Miguel trained his Monday clients for a total of 6 hours and his Tuesday clients for a total of 7 hours. How long does each of the workout plans last?

length of each plan A work out: ___ hours
length of plan B work out:__ hours

Answer 1

length of each plan A work out: 1 hour

length of plan B work out:
`(1)/(2)` hours

Explanation:

Let x represents the time taken to do plan A

y represents the time taken to do plan B

On Monday there were 5 clients who did Plan A and 2 who did Plan B.

Miguel trained his Monday clients for a total of 6 hours

5x + 2y = 6 -----------> equation 1

On Tuesday there were 3 clients who did Plan A and 8 who did Plan B. .He trained his Tuesday clients for a total of 7 hours

3x + 8y = 7 -------------------> equation 2

Now we solve for x and y

Let multiply the first equation by -4 to eliminate y

-20x -8y = -24

3x + 8y = 7

------------------------ (add both equations)

-17x = -17

Divide both sides by -17

So x= 1

Plug in 1 for x in first equation and solve for y

5x + 2y = 6

5(1) + 2y = 6

5 + 2y =6

Subtract 5 on both sides

2y = 1

y = 1/2

length of each plan A work out: 1 hour

length of plan B work out:
`(1)/(2)` hours