Three pipes with a consistent flow fill a tank. The first two pipes fill the tank at the same time, while the third pipe fills the tank alone. The tank is filled 5 hours quicker by the second pipe and 4 hours slower by the third pipe. The first pipe takes the following amount of time:
A. 6hours
B. 10hours
C. 15hours
D. 30hours
Answer:C
Three pipes with a consistent flow fill a tank. The first two pipes fill the tank at the same time, while the third pipe fills the tank alone. The tank is filled 5 hours quicker by the second pipe and 4 hours slower by the third pipe. The first pipe takes the following amount of time:
A. 6hours B. 10hours C. 15hours D. 30hours
Explanation: Assume that filling the tank with just the first pipe takes x hours.The second and third pipes will take (x -5) and (x - 9) hours to fill the tank, respectively.1/x + 1/(x - 5) = 1/(x - 9) x - 5 + x/ x(x-5) = 1/(x - 9) (2x - 5)(x - 9) = x(x - 5) x2 - 18x + 45 = 0 (x - 15)(x - 3) = x(x - 5) x2 - 18x + 45 = 0 x [ignoring x = 3].