一條好難既數學題,急

Two taps A and B are used to fill up a tank with water. If tap A isused alone to fill up the tank, it takes 25 minutes longer than using tap Balone. If each of tap A and tap B is turned on alone for 20 minutes one by oneand then they are turned on together for 10 minutes, the tank will be full.
(a)Find the time taken for tap A alone to fill up the tank.
(b)Find the time taken for tap B alone to fill up the tank.


(a)
Let t minutes be the time taken for tap A alone to fill up the tank.
Then, the time taken for tap B alone to fill up the tank = (t - 25) minutes

Then, fraction of the tank that filled by tap A alone = 1/t
and fraction of the tank that filled by tap B alone = 1/(t - 25)

To fill up the tank:
(1/t)*20 + [1/(t - 25)] * 20 + {(1/t) + [1/(t - 25)]} * 10 = 1
(30/t) + [30/(t - 25)] = 1
[30(t - 25)/t(t - 25)] + [30t/t(t - 25)] = 1
(30t - 750 + 30t)/(t² - 25t) = 1
60t - 750 = t² - 25t
t² - 85t - 750 = 0
(t - 75)(t - 10) = 0
t = 75 or t = 10 (rejected for 10 - 25 < 0)
Hence, it takes 75 minutes for tap A alone to fill up the tank.

(b)
t - 25 = 50
Hence, it takes 50 minutes for tap B alone to fill up the tank.