Question

A swimming pool is filled by 3 pipes with uniform flow. First two pipes operating
simultaneously, fill the pool in the same time during which the pool is filled by the third pipe
alone. Second pipe fills the pool 5 hrs. faster than the first pipe and 4 hrs. slower
than the third pipe. Find the time required by each pipe to fill the pool separately.​

Answer 1

Answer:

15 , 10 & 6 Hrs

Step-by-step explanation:

Let say Slowest Pipe (First) Fill The Pool in  P Hrs

Then Second Pipe Fill the pool in P - 5 Hrs

Fastest ( third) Pipe fill teh Pool in  P - 5 - 4 = P - 9 hrs

Tank fille in 1 hrs by 1st & 2nd Pipe in 1hr

= 1/P  + 1/(P - 5)  

Tank filled by third pipe in 1 hr = 1/(P - 9)

Equating both as per Question dat

=>  1/P  + 1/(P - 5)    = 1/(P - 9)

=> (2P-5)(P - 9) = P (P - 5)

=> 2P² - 23P + 45 = P² - 5P

=> P² - 18P + 45 = 0

=> P² - 15P - 3P + 45 = 0

=> P(P - 15) -3(P -15) = 0

=> (P -15)(P -3) = 0

=> P = 15  & P = 3

P = 3 not possible as then P-5 & P-9 would be -ve

=> P = 15

=> Slowest Pipe fill the pool in 15 Hrs

Second Pipe in 10 hrs

Fastest Pipe in 6 hrs

Answer 2

Answer:

Step-by-step explanation: