One pipe can fill a tank in four hours; another pipe can fill the same tank in three hours.?
How long will it take to fill the tank if both pipes filled it at the same time? Give answer as a fraction
8 Answers
 davidLv 76 months agoBest Answer
Rate for 1st = 1/4 tank/hr
Rate for 2nd = 1/3 tank /hr
... mult. each by time to get how much it fills
... add to = 1 (need to fill 1 tank)
(1/4)t + (1/3)t = 1 >>> get common denom.
3t/12 + 4t/12 = 1
7t/12 = 1
t = 12/7 hours
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 ComoLv 76 months ago

Let volume of tank be V m³
Rate for pipe 1 = V/4 m³/h
Rate for pipe 2 = V/3 m³/h
Combined rate = 7V/12 m³/h
Time to fill = V / ( 7V/12) = 12/7 = 1•7 hours = 1 h 42 min
 Ian HLv 76 months ago
Add rates in terms of fraction of a tank per hour.
1/4 + 1/3 = 7/12 of a tank per hour, so takes 12/7 hours to fill 1 tank
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 Φ² = Φ+1Lv 76 months ago
The first pipe can fill 3 tanks in 12 hours, while the second pipe can fill 4 tanks in 12 hours.
Together they can fill 7 tanks in 12 hours, which is 1 tank in 12/7 hours.
 AmyLv 76 months ago
Least common multiple of 3 and 4 is 12.
In 12 hours, the first pipe can fill 3 tanks and the second pipe can fill 4 tanks.
Thus the two pipes together can fill 7 tanks in 12 hours.
Filling 1 tank takes 12/7 hours.
 冷眼旁觀Lv 66 months ago
Let t hours be the time taken to fill the tank if both pipes filled at the same time.
The first pipe fills 1/4 of the tank in one hour.
The second pipe fills 1/3 of the tank in one hour.
[(1/4) + (1/3)] × t = 1
[(3/12) + (4/12)] × t = 1
(7/12)t = 1
t = 12/7
t = 1_(5/7)
It takes 1_(5/7) hours.
I agree with you. You explained well. Good job