我岀一條小學三年級數學題考考大家......10分

Question

A\\B\\C三个阀门同时放水,要1小时能蓄满水池.如果A\\C同时放水需要1.5小时蓄满,如果C\\B同时放水需要2小时蓄满.问:A\\B同时放水需要几小时放满?

Answer 1

首先假設 A, B 和 C 各自的注水速度分別為 Ra, Rb 和 Rc.

咁從比左的資可以得出以下數式:

1/(Ra + Rb + Rc) = 1 (三個一齊注水)
1/(Ra + Rc) = 1.5 (A 和 C 一齊注水)
1/(Rb + Rc) = 2 (B 和 C 一齊注水)

求它們的倒數可知:
Ra + Rb + Rc = 1 --> (1)
Ra + Rc = 2/3 --> (2)
Rb + Rc = 1/2 --> (3)

(2) + (3) - (1) 可得出:
Rc = 1/6
代入 (1) 就得到:
Ra + Rb = 5/6

所以如果 A 和 B 同時注水所需時間為:
1/(Ra + Rb) = 6/5, 即 1.2 小時 或 1 小時 12 分

Answer 2

係呢題數度睇到,,
(A/C)要多0.5hour就可以搞掂左(B)係1hour既注水。
(A/C)(0.5)=(B)(1)
咁即係(A/C)係(B)既2倍..
就知道(B)係個1hour中,,
只係搞掂左1/3,,其餘(A/C)搞掂2/3..
從條"色"我地知:A>B>C
所以:(B)(1hour)=1/3(水池)
(A)(1hour)>1/3(水池)
(C)(1hour)<1/3(水池)
我地假設水池有900(L)水,,
B(1hour)=300(L)
A(1hour)>300(L)
C(1hour)<300(L)
(B/C)同時放水要2HOURS,,
所以:B(2)=300(L)X2=600(L)
C(2)=900(L)-600(L)=300(L)
C(1)=300(L)/2=150(L)
用番之前GE"色",,
A=900(L)-300(L)-150(L)=450(L)
得到GE"色"係
900/750(hours)=1.2(hours)

Answer 3

1.2 hour to fill the tank

Answer 4

abc三个阀门同时放水,mean will spit out 3time要1小时能蓄满水池3x10=30a c需要1.5小时蓄满C\B同时放水需要2小时蓄满.问:A\B同时放水需要几小时放满? 2 hour

2006-12-15 11:41:38 補充：
is 1.2

Answer 5

I think this is how a 3rd grade student would answer:

A,B and C fill one tank in an hour,
A and C fill 1/1.5 tank in an hour, so in hour hour B fills 1-1/1.5=1/3 tanks, or it takes B three hours to fill one tank.
Similarly, A fills 1-1/2=1/2 tank in one hour, or it takes A 2 hours to fill one tank.
So if A and B fill a tank together, they will fill 1/3+1/2=5/6 tank in an hour.
So it will take 6/5=1.2 hour to fill the tank.

Answer 6

Let V be the volume of the pool and a, b, c be the influx rate at volume/time. Then

V / (a + b + c) = 1 ----------- (1)
V / (a + c) = 3 / 2 -------------- (2)
V / (b + c) = 2 ----------------- (3)
Divide (2) by (1)
(a + c) / (a + b + C) = 2 /3 ---- (4)

Devide (3) by (1)
(b + c) / (a + b + c) = 1 / 2 ---- (5)

(4) + (5)
(a + b + 2c) / (a + b + c) = 7 / 6
[2(a + b + c) - (a + b)] / (a + b + c) = 7 / 6
2 - (a + b) / (a + b + c) = 7 / 6
(a + b) / (a + c + c) = 5 / 6 ----- (6)

Divide (1) by (6)
V / (a + b) = 6 / 5
Therefore, it takes 1.2 hrs to fill in the pool by opening gates A and B

Is it really a mathematics question for Primary 3 ??? How can a P.3 student solve this problem, I don't believe at all

2006-12-15 10:38:11 補充：
There is a typing error, eqt (6) should be(a + b) / (a + b + c) = 5 / 6

Answer 7

1/(1/a+1/b+1/c)=1 => 1/a+1/b+1/c=1
1/(1/a+1/c)=1.5 => 1.5(1/a+1/c)=1 => 1.5(1-1/b)=1 => b=3
1/(1/b+1/c)=2 => 2(1/b+1/c)=1 => 2(1-1/a)=1 => a=2
Ans. of the eqt. is
1(1/a+1/b) = 6/5 =1.2hrs