時間與工作 - 例題解析

題1 - A單獨完成一項工作需要8天，B單獨完成需要10天。兩人合作完成需要多長時間？

答案 - A

解釋

A's 1 day work= 1/8, B`s 1 day work = 1/10
∴ (A+B) 1 day work = (1/8+1/10) = 9/40
Both cooperating can complete it in 40/9 days.

題2 - A和B一起挖一條溝需要12天，A單獨挖需要30天。B單獨挖需要多長時間？

答案 - C

解釋

(A+B)'s 1 day work = 1/12, A's 1 day work =1/30 
∴ B's 1 day work = (1/12-1/30) = 3/60 = 1/20 
Henceforth, B alone can dive the trench in 20 days.

題3 - A完成一項工作需要25天，B完成需要20天。兩人合作工作5天后，A離開了。B還需要多長時間才能完成剩餘的工作？

答案 - D

解釋

(A+B)'s 5 days work = 5(1/25+1/20) = (5*9/100) = 9/20 
Remaining work = (1-9/20) = 11/20 
1/20 work is finished by B in 1 day 
11/20 work is finished by B in (1*20*11/20) = 11 days

題4 - A和B一起完成一項工作需要12天，B和C一起需要15天，C和A一起需要20天。三人合作完成需要多長時間？此外，A單獨完成需要多長時間？

答案 - A

解釋

(A+B)'s 1 day work = 1/12, 
(B+C)'s 1 day work = 1/15,
(C+A)'S 1 day work = 1/20 
Including: 2(A+B+C)'s 1 day work = (1/12+ 1/15+ 1/20)= 12/60 = 1/5 
∴ (A+B+C) `s 1 day work = (1/2 *1/5) = 1/10 
∴ working together they can complete the work in 10 days. 
A's 1 day work = (1/10-1/15) = 1/30, B`s 1 day work = (1/10-1/20) = 1/20 
C's 1 day work = (1/10-1/12) = 1/60 
∴ A alone can take the necessary steps in 30 days.

題5 - A可以30天建好一堵牆，B單獨需要40天。如果他們一起建造並獲得7000元報酬，B應該分多少錢？

答案 - B

解釋

A's 1 days work = 1/30,
B's 1 day work = 1/40,
Proportion of their shares = 1/30:1/40 = 4:3
B's offer = (7000*3/7) = Rs. 3000

題6 - A完成一項工作需要10天，B單獨需要15天。他們合作5天后，剩下的工作由C在2天內完成。如果他們總共獲得4500元報酬，他們應該如何分配這筆錢？

答案 - B

解釋

(A+B)'s 5 days work = 5(1/10+ 1/15)= (5* 1/6)= 5/6 
Remaining work = (1-5/6) = 1/6 
C's 2 days work = 1/6 
(A's 5 day work): (B's 5 day work): (C's 2 days work) 
= 5/10: 5/15: 1/6 
= 15: 10:5 = 3:2:1 
A's offer = (4500*3/6) = Rs. 2250
B's offer = (4500*2/6) = Rs. 1500 
C's share= (4500*1/6) = Rs. 750

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