(f.5)Equations 應用題2條

45.
Let v km/h the speed of the ship in still water.

[840/(v + 3)] + [840/(v - 3)] = 37.5
[840(v - 3) + 840(v + 3)] / (v + 3)(v - 3) = 37.5
[840v - 2520 + 840v + 2520] / (v² - 9) = 37.5
1680v = 37.5v² - 337.5
5v² - 224v - 45 = 0
(v - 45)(5v + 1) = 0
v = 45 or v = -1/5 (rejected)

Time needed for the ship travelled from town A to town B
= 840 / (45 + 3) h
= 17.5 h

(6:00 + 17:30) - 12:00 = 11:30
The time when the ship arrived at town B = 11:30 p.m.


46.
(a)
Let a minutes be the time needed for tap A alone to fill up the tank,
and b minutes be the time needed for tap B alone to fill up the tank.

b = a - 25 ...... [1]
20(1/a) + 20(1/b) + 10(1/a + 1/b) = 1 ...... [2]

From [2] :
(30/a) + (30/b) = 1
(30b + 30a)/ab = 1
30a + 30b = ab ...... [3]

Put [1] into [3] :
30a + 30(a - 25) = a(a - 25)
30a + 30a - 750 = a² - 25a
a² - 85a + 750 = 0
(a - 75)(a - 10) = 0
a = 75 or a = 10 rejected

Time taken for tap A alone to filled up the tank = 75 minutes

(b)
Put a = 75 into [1] :
b = 75 -25
b = 50

Time taken for tap B alone to filled up the tank =50 minutes

2012-11-01 22:53:52 補充：
1/a : 用 tap A 每分鐘裝滿 1/a tank
1/b : 用 tap B 每分鐘裝滿 1/b tank

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