Question

Pipe p (inlet) and pipe q ( outlet) can fill a tank completely in 10 hours while pipe q ( outlet) and pipe r ( inlet) can empty that tank in 5 hours. if pipe p and r together fill that tank in 10/7 hours, what is the time taken by pipe r alone to fill that tank?​

Answer 1

r alone can fill in 5 hrs

Step-by-step explanation:

Pipe p (inlet) and pipe q ( outlet) can fill a tank completely in 10 hours

=> 1/p  -  1/q  = 1/10

pipe q ( outlet) and pipe r ( inlet) can empty that tank in 5 hours

=> 1/q - 1/r  =  1/5

Adding both

1/p  - 1/r  = 1/10 + 1/5

=> 1/p - 1/r  = 3/10

if pipe p and r together fill that tank in 10/7 hours

=>  1/p  + 1/r  = 7/10

=> 2/r = 7/10 - 3/10

=> 2/r = 4/10

=> 1/r = 2/10

=> r = 5

r alone can fill in 5 hrs

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