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
- davidLv 78 months agoFavorite 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
others did this in different ways, but I am the only one who explained it so you can learn to do more ... this is the BEST ANSWER
- ComoLv 78 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 78 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
- Mike GLv 78 months ago
t/4+t/3 = 1
7t = 12
t = 12/7 hours
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- Φ² = Φ+1Lv 78 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 78 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 68 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.
- King LeoLv 78 months ago
¼ + ⅓ = 7/12
time = 1/ (7/12 ) = 12/7 hrs