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