Keiko 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 3 clients who did plan a and 2 who did plan b. on thursday there were 5 clients who did plan a and 6 who did plan b. keiko 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?

length of each plan a workout: hour(s)

lenght of each plan b workout: hour(s)

Hey!

Hope this helps

Given Information:

No client can do both Plans

On Wednesday: 3 clients did Plan A, and 2 clients did Plan B

On Thursday: 5 clients did Plan A, and 6 clients did Plan B

Keiko was training for a total of 6 hours on Wednesday, and training for a total of 12 hours on Thursday

We'll let t stand for length of time

Wednesday:

3t + 2t = 6

5t = 6

t = 1.2 hours > translates to 1 hour, and 12 minutes

On Wednesday, she was with her clients individually for 1 hour and 12 minutes

Thursday:

5t + 6t = 12

11t = 12

t ~ 1.1 hours > translates to about 1 hour and 6 minutes

On Thursday, she was with her clients individually for about 1 hour and 6 minutes

We'll let A stand for total length of time for Plan A, and B stand for total length of time for Plan B

We'll let W stand for Wednesday, and T stand for Thursday...

We'll let z stand for total amount of clients for that plan...

We know, for Plan A, on Wednesday there were 3 clients, and Thursday there were 5 clients

We also know for Plan B, on Wednesday there were 2 clients, and Thursday there were 6 clients

(3W + 5T)/z = A

(3(1.2) + 5(1.1))/8 = A

(3.6 + 5.5)/8 = A

9.1/8 = A

Plan A = 1.1375 hours > 1 hour 8 minutes 15 seconds

(2W + 6T )/z ~ B

(2(1.2) + 6(1.1))/8 ~ B

(2.4 + 6.6)/8 ~ B

9/8 ~ B

Plan B ~ 1.125 hours > 1 hour 7 minutes 30 seconds

When ever the symbol " ~ " is used in an equation, it stands for "About"...

Sorry for the mess up before