Question 1189831: Espano
Joe 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 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Joe trained his Monday clients for a
total of 10 hours and his Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = length of workout A
y = length of workout B
time length durations are in hours
Monday:
3 clients for workout A
5 clients for workout B
3x = time for just the plan A people
5y = time for just the plan B people
3x+5y = total time for everyone on monday
3x+5y = 10 hours
Tuesday:
6 clients for plan A
2 clients for plan B
6x = time for just the plan A people
2y = time for just the plan B people
6x+2y = total time for everyone on tuesday
6x+2y = 10
------------------------------------
We found that
3x+5y = 10
6x+2y = 10
for monday and tuesday respectively
There are a number of ways we can solve this system of equations.
I'll use the substitution method.
In this method, there are a few routes as well.
Let's solve for y in the second equation
I'm picking this because it means we avoid messy decimals.
6x+2y = 10
2y = 10-6x
2y = -6x+10
y = -6x/2+10/2
y = -3x+5
Substitute that into the first equation. Then isolate x.
3x+5y = 10
3x+5(-3x+5) = 10
3x-15x+25 = 10
-12x+25 = 10
-12x = 10-25
-12x = -15
x = -15/(-12)
x = 5/4
x = 1.25
We get a decimal value, but at least it's not something too crazy.
Workout A takes 1.25 hours
aka 1 hour, 15 minutes
Then,
y = -3x+5
y = -3*1.25+5
y = -3.75+5
y = 1.25
Coincidentally, we get the same value as x.
It won't always be the case that x = y.
Answers:
Plan A takes 1.25 hours
Plan B takes 1.25 hours
1.25 hours = 1 hr, 15 min
|
|
|
