two taps A and B are used to fill up a tank with water. If tap A is used alone to fill up the tank, it takes 25 minutes longer than using tap B alone. If each of tap A and tap B is turned on alone for 20 mintues one by one and 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.
I want full solution (indcluding working) and explanation if possible.
Thx!
F.5 math
2011-04-16 3:50 am
回答 (1)
2011-04-16 6:34 am
✔ 最佳答案
The rate of tap A and B are 1/(x + 25) and 1/x respectively.So, 20[1/(x + 25) + 1/x] + 10[1/(x + 25) + 1/x] = 1
1/(x + 25) + 1/x = 1/30
x(x + 25) = 30(2x + 25)
x^2 - 35x - 750 = 0
(x - 50)(x + 15) = 0
x = -15 or x = 50
So, tap A will need 75 mins to fill up the tank alone.
(b) tap B will need 50 mins to fill up the tank alone.
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