- 能力傾向有用資源
- 能力傾向 - 問答
管道與水箱 - 例題解析
題1 - 兩個水管A和B分別可以單獨充滿一個水箱，A需要24小時，B需要30小時。如果同時開啟這兩個水管，裝滿空水箱需要多長時間？
答案 - B
解析
Part filled by A in 1 hour = 1/24, part filled by B in 1 hour = 1/30 Part filled by (A+B) in 1 hour = (1/24+ 1/30) = 9/120 = 3/40 Time taken by both to fill the tank = 40/3 hrs = 13 hrs 20 min.
題2 - 一個漏斗可以15小時充滿一個水箱。由於底部有一個洞，實際需要20小時才能充滿。如果水箱已滿，這個洞需要多長時間才能排空？
答案 - C
解析
Work done by the break in 1 hour = (1/15-1/20) = 1/60 Time taken by the break to discharge it = 60 hours
題3 - 漏斗A和B分別可以在6小時和9小時內充滿一個水箱，漏斗C可以在12小時內排空。如果同時開啟所有三個漏斗，空水箱需要多長時間才能裝滿？
答案 - B
解析
Net part filled in 1 hour = (1/6+1/9+1/12) = 7/36 Thus, the tank will be full in 36/7 hrs.
題4 - 兩個水管A和B分別可以在24分鐘和32分鐘內充滿一個水箱。如果同時開啟兩個水管，那麼在多少分鐘後關閉水管B，才能使水箱在18分鐘內充滿？
答案 - B
解析
Let B be shut after x minutes. At that point, (part filled by (A+B) in x min.)
+ {part filled by A in (18-x) min} = 1
∴ x (1/24+ 1/32) + (18-X)*1/24 = 1
=> 7x/96 + (18-x)/24 =1
=> 7x+4(18-x) = 96
=> 3x= 24
=> x = 8
Subsequently, B ought to be shut after 8 min.
題5 - 兩個水管A和B分別可以在1小時和75分鐘內充滿一個水箱。還有一個排水管C。如果同時開啟三個水管，水箱在50分鐘內充滿。排水管C排空一個滿水箱需要多長時間？
答案 - C
解析
Work done by C in 1 min. = (1/60 +1/75-1/50) = 3/300 = 1/100 Thus, C can discharge the full tank in 100 minutes.
題6 - 兩個水管分別可以在14小時和16小時內充滿一個水庫。同時開啟水管，由於底部洩漏，實際需要多花32分鐘才能充滿水庫。水庫裝滿後，洩漏需要多長時間才能排空整個水庫？
答案 - C
解析
Work done by the two funnels in 1 hour= (1/14+ 1/16) = 15/112 Time taken by these funnels to fill the tank = 112/15 hrs = 7 hrs 28 min. Because of spillage, time taken = 7 hrs. 28 min. + 32 min. = 8 hrs. ∴ Work done by (two funnels + spill) in 1 hour = 1/8 Work done by the break in 1 hour = (15/112-1/8) = 1/112 Break will discharge the full reservoir in 8 hours.
aptitude_pipes_cisterns.htm
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