The time taken to empty the pool is 28 hours. This is obtained by taking a variable x as the time taken by both pumps combined for emptying 1/3 rd of the pool and y as the time taken by first pump to empty the remaining.
Given the first pump can empty the pool in 36 hours.
⇒Rate of the first pump is 1/36
The rate of the second pump is twice faster; that is 2×(1/36)=1/18
The rate of both pumps combined will be (1/36 + 1/18)
Let x be the time taken by both pumps combined for emptying 1/3 rd of the pool and y be the time taken by first pump to empty the remaining.
If both pumps are working combined,
(1/36 + 1/18)x = 1/3
⇒x = 4 hours
The first pump filling the remaining after the second pump broke,
(1/36)y = 2/3
⇒y = 24 hours
Therefore, the total time taken to empty the pool is x+y=4+24=28 hours
Hence the total time taken to empty the pool is 28 hours
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