SOLUTION: a tank can be filled in 3 hours with a pipe.It can be filled in 5 hours with another pipe and it can be drained (if full) in 7 hrs by an emergency valve.How many hours will it take

Question 923884: a tank can be filled in 3 hours with a pipe.It can be filled in 5 hours with another pipe and it can be drained (if full) in 7 hrs by an emergency valve.How many hours will it take to fill the tank if both the pipes and the emergency valve are opened simultaneously?
a)4.32
b)3.52
c)2.56
D)none
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
rate = v/t
---
x = pipe-1 rate = v/3
y = pipe-2 rate = v/5
z = drain rate = v/7
---
x + y + z = v/3 + v/5 - v/7
x + y + z = 5*7v/3*5*7 + 3*7v/3*5*7 - 3*5v/3*5*7
x + y + z = 35v/105 + 21v/105 - 15v/105
x + y + z = 41v/105
x + y + z = (41/41)v/(105/41)
x + y + z = v/(105/41)
x + y + z = rate = v/t = v/(105/41)
---
t = 105/41
t = 2.561 hours
---
answer:
c)2.56
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