Problem Solving

A water tank has four inlets. Through the first three inlets, the tank can be filled in 12 minutes. Through the second, third and fourth inlets, the tank can be filled in 15 minutes. Through the first and fourth inlets, the tank can be filled in 20 minutes. How much time in minutes will it take for all the four inlets working together to fill the tank?

A. 5
B. 8
C. 10
D. 15
E. 16

Let the work done by inlets per hour be a, b, c and d

a + b + c = 1/( \(\frac{1}{5}\) hour) = 5

b + c + d = 4

a + d = 3

Adding d to both sides of equation 1) and adding a to both sides of equation 2), we get

a + b + c + d = 5 + d = 4 - a
Hence, a - d = 1
Combining this with equation 3), we get
a = 2
d = 1
b + c = 3
a + b + c + d = 6 = 1/( \(\frac{1}{6}\) hour)

Hence, time taken = \(\frac{1}{6}\) hour = 10mins