Answer:
The time duration of the two pipes restricted flow before the flow became normal is 4.5 minutes
Step-by-step explanation:
The given information are;
The time duration for the volume, V, of the basin to be filled by one of the pipe, A, = 12 minutes
The time duration for the volume, V, of the basin to be filled by the other pipe, B, = 16 minutes
Therefore, the flow rate of pipe A = V/12
The flow rate of pipe B = V/16
Due to the restriction, we have;
The proportion of its carrying capacity the first pipe, A, carries = 7/8 of the carrying capacity
The proportion of its carrying capacity the second pipe, B, carries = 5/6 of the carrying capacity
Whereby the tank is filled 3 minutes after the restriction is removed, we have;
![\dfrac{7}{8} \times \dfrac{V}{12} \times t + \dfrac{5}{6} \times \dfrac{V}{16} \times t + \dfrac{V}{12} \times 3 + \dfrac{V}{16} \times 3 = V](https://tex.z-dn.net/?f=%5Cdfrac%7B7%7D%7B8%7D%20%5Ctimes%20%5Cdfrac%7BV%7D%7B12%7D%20%5Ctimes%20t%20%2B%20%5Cdfrac%7B5%7D%7B6%7D%20%5Ctimes%20%5Cdfrac%7BV%7D%7B16%7D%20%5Ctimes%20t%20%2B%20%20%5Cdfrac%7BV%7D%7B12%7D%20%5Ctimes%203%20%2B%20%5Cdfrac%7BV%7D%7B16%7D%20%5Ctimes%203%20%3D%20V)
Simplifying gives;
![\dfrac{(2\cdot t +7) \cdot V}{16} = V](https://tex.z-dn.net/?f=%5Cdfrac%7B%282%5Ccdot%20t%20%2B7%29%20%5Ccdot%20V%7D%7B16%7D%20%20%3D%20V)
2·t + 7 = 16
t = (16 - 7)/2 = 4.5 minutes
Therefore, it took 4.5 seconds of the restricted flow before the the flow of water in the two pipes became normal