SOLUTION: Please help.... I posted this question 19239 because I'm helping my daughter. Sally paint a garge in 8 hours and Susan can paint the garage in 6 hours. If they paint together

Question 19283: Please help....
I posted this question 19239 because I'm helping my daughter. Sally paint a garge in 8 hours and Susan can paint the garage in 6 hours. If they paint together how long will it take. I have 1 hour and 15 minutes is this correct.
Thanks very much.
Found 2 solutions by Earlsdon, mmm4444bot:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
No, sorry! First, you should find the rate (how much of the garage per hour) at which the two can paint the garage.
If Sally can paint the garage in 8 hours, then she can paint 1/8 of the garage in 1 hour.
If Susan can paint the garage in 6 hours, then she can paint 1/6 of the garage in 1 hour.
So, together, they can paint (1/8 + 1/6) = 7/24 of the garage in 1 hour.
Let G stand for the painting of the entire garage
You could write this as: (7/24)G = 1 hour. You need to find the value of G, so multiply both sides by the multiplicative inverse of 7/24, that's 24/7.
Now you have G = 24/7 hours. This is the time required for both Sally & Susan to paint the the garage together.
24/7 hours = 3 hr, 25 mins, 43 secs.
Answer by mmm4444bot(95) (Show Source): You can put this solution on YOUR website!
Hello There:
In work problems like this, we need to approach is in terms of how much of the job is done per unit of time.
Sally paints the garage in 8 hours, so each hour she completes 1/8th of the job.
Susan paints the garage in 6 hours, so each hour she completes 1/6th of the job.
Working together, they complete (1/8 + 1/6)th of the job per hour.
1/8 + 1/6 = 7/24
Completing 7/24ths of the job each hour means that it takes 24/7th hours when working together.
24/7 = 3.4286
0.4286*60 = 25.7
It takes them 3 hours and 25.7 minutes to do the job.
~ Mark

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