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oakhan oakhan
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11 years ago
John is mixing a saline solution. He has 4 gallons of a 70%solution. How many gallons of a 32% solution does he need to created a 58% saline solution?

I have another question.

Sally and Paul can paint a room in 6 hours. Paul working alone can paint the room 2 hours quicker than sally. How long does it take each of them to paint the room working alone?
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#1
11 years ago
1) Assuming the percentage solution is volume/volume (otherwise is a very challenging problem)

Initial amount of salt
4*.7 = 2.8 gal salt
Let V = volume added of the 32% solution
(2.8 + 0.32V)/(4 + V) = 0.58
(4 + V)0.58 = 2.8 + 0.32V
0.26V = 0.48
V = 1.85 gal

2)
Let
S = Sally speed
P = Paul speed
A = Total area painted
t = time to finish painting
t = A/(S + P)
A/(S + P) = 6
2A/P = A/S
P/A = 2S/A
1/6 = P/A + S/A
1/6 = P/A + P/2A

P/A = 1/9
It takes Paul 9 hours to paint it by himself

S/A = 1/18
It takes Sally 18 hours to paint it by herself
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