Two taps A and B are used to fill up a tank with water.It takes 25mins longer when tap A is used alone to fill the tank than tank B.If each of Tap A and Tap B is turned on successively for 20mins and then they are turned on together
for 10mins ,the tank is full.Find the time needed for Tap A alone and Tap B alone to fill up the tank.
Slow the steps clearly
F.4 quadratic equaations in one unknown
2008-09-25 2:36 am
回答 (1)
2008-09-25 5:38 am
✔ 最佳答案
Let time needed by B alone = x minutes.Time needed by A alone = (x + 25) min.
Time B is on = 20 + 10 = 30 min. So B filled 30/x of the tank.
Time A is on = 20 + 10 = 30 min. So A filled 30/(x + 25) of the tank.
Together they filled up the tank, that is
30/x + 30/(x +25) = 1
30(x + 25) + 30x = x(x + 25)
30x + 750 + 30x = x^2 + 25x
x^2 - 35x - 750 = 0
(x - 50)(x + 15) = 0
x = -15 (rej.) and 50 min.
So time for B alone = 50 min. Time for A alone = 75 min.
收錄日期: 2021-04-25 22:37:48
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