Ned !
john 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 friday there were 3 clients who did plan a and 5 who did plan b. on saturday there were 9 clients who did plan a and 7 who did plan b. john trained his friday clients for a total of 6 hours and his saturday clients for a total of 12hours. how long does each of the workout plans last?

They are both the same at 3/4 of an hour

Step-by-step explanation:

We have a system of equations here.  The first one is for Friday:

3A + 5B = 6, which says that 3 people at the number of hours for plan A plus 5 people at the number of hours for plan B equals 6 hours total.

The second equation is for Saturday:

9A + 7B = 12, which says that 9 people at the number of hours for plan A plus 7 people at th number of hours for plan B equals 12 hours total.

We can solve this easily using the addition/elimination method.  Begin by multipying the first equation through by a -3 to eliminate the A's.  That gives you a new first equation of:

  -9A  -  15B  =  -18

  9A  +    7B  =  12

You can see that the A's are eliminated, and adding what remains leaves us with

-8B = -6 so

B = 3/4 hour

Now we can sub that back in for B in either one of our original equations to solve for A.  I changed the 3/4 to .75 for ease of multiplying:

9A + 7(.75) = 12 and

9A + 5.25 = 12 and

9A = 6.75 so

A = .75 which is also 3/4 of an hour

29.5977692753

step-by-step explanation: