From http://www.sgforums.com/forums/2297/topics/348909
A rectangular pool can be filled by two pipes together in 6 hours. The smaller pipe alone takes 5 hours longer than the larger pipe to fill the pool. Find them time each pipe will take to fill the pool on its own.
Answer:
Let the time taken by small pipe alone = Ts
Let the time taken by bigger pipe alone = Tb
Let Volume of pool = V
So
Rate of flow of small pipe = V/Ts
Rate of flow of bigger pipe = V/Tb
Get the equations out
Ts - Tb = 5
Ts = Tb + 5 ------------- (1)
V / ( V/Ts + V/Tb) = 6
TsTb / (Ts + Tb) = 6
Ts Tb = 6Ts + 6 Tb
Sub (1) into equation
Tb² + 5Tb = 6Tb + 30 + 6 Tb
Tb² - 7Tb - 30 = 0
Solving, Tb = 10 hours or -3 (reject)
Hence, Ts = 15 hours
