Two pipes running together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Answers
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Pipes will fill tank in 10 & 15 mins
Step-by-step explanation:
Let say pipe 1 take time to fill cistern = A mins
then Pipe 2 will take time to fill cistern = A + 5 Mins
Tank filed by pipe 1 in 1 min = 1/A
Tank filed by pipe 2 in 1 min = 1/(A + 5)
Tank filled by both pipes in 1 Min = 1/A + 1/(A + 5)
= (A + 5 + A)/A(A+5)
= (2A + 5)/A(A+ 5)
Tank filled by both pipes in 6 mins
filled in1 min = 1/6
=> (2A + 5)/A(A+ 5) = 1/6
=> 12A + 30 = A² + 5A
=> A² - 7A - 30 = 0
=> A² - 10A + 3A - 30 =0
=> A(A - 10) + 3(A - 10) =0
=> (A + 3)(A - 10) = 0
A = 10
A + 5 = 15
Pipes will fill tank in 10 & 15 mins
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