Question

Nicole 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 6 who did Plan B. On Thursday there were 3 clients who did Plan A and 2 who did Plan B. Nicole trained her Wednesday clients for a total of 7 hours and her Thursday clients for a total of 3 hours. How long does each of the workout plans last?

Answer 1

I have a feeling I've seen this question before
anyway

A=number of hours that plan A is
B=number of hours that plan B is

so

on wednesday, 7hr
5A and 6B so
5A+6B=7

on thursday, 3 hours
3 of A and 2  of B
3A+2B=3


so we gots

5A+6B=7
3A+2B=3

elimination
eliminate B's
multiply 2nd equation by -3 and add to 1st equation

5A+6B=7
-9A-6B=-9 +
-4A+0B=-2

-4A=-2
divide both sides by -4
A=1/2
A=0.5

sub back

3A+2B=3
3(0.5)+2B=3
1.5+2B=3
minus 1.5 both sides
2B=1.5
divide by 2 both sides
B=0.75


plan A lasts 1/2 hour or 0.5 hour or 30 mins
plan B lasts 3/4 hour or 0.75 hour or 45 mins

Answer 2

Plan A = 30 minutes
Plan B = 45 minutes
Hope that helps <3