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Answer:
Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Step-by-step explanation:
Let tap B fills the pool alone in the time = x hours
So in one hour part of pool will be filled =
Another tap A when turned on, it takes time to fill the pool = x-5 hours
So in one hour part of the same pool filled =
Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.
Part of the pool filled in one hour by both the taps =
Now we form an equation
Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on
3(x - 4) = x(x - 5)
x² -5x = 3x - 12
x² - 8x + 12 = 0
x² - 6x - 2x + 12 = 0
x(x - 6) - 2(x - 6) = 0
(x -2)(x - 6) = 0
x = 2, 6 hours
We will take higher value of x as x = 6 hours for tap B.
Time taken by tap A = 6 - 4 = 2 hours.
Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.