SOLUTION: If Fran were to paint her living room alone it would take 6 hours. Her sister could do the job in 8 hours. How long would it take them working together?

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Question 918080: If Fran were to paint her living room alone it would take 6 hours. Her sister could do the job in 8 hours. How long would it take them working together?
Found 2 solutions by richwmiller, Hawksfan:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/a+1/b=1/x
1/6+1/8=1/x
8/48+6/48=1/x
14/48=1/x
x=48/14
x=3.42857143 hours working together
check
x/a+x/b=1
x/6+x/8=1
3.42857143/6+3.42857143/8=1
0.57142857+0.42857143=1
1.0=1
ok
codewt

Answer by Hawksfan(61) About Me  (Show Source):
You can put this solution on YOUR website!
r1 =6
r2 =8
t = ?
[(1/r1) * t] + [(1/r2)*t] = 1
t/6 + t/8 = 1
multiply by common denominator... 24
24 (t/6 + t/8 = 1)
4t + 3t =24
7t = 24
t = 24/7 = 3.4hrs