- 能力倾向有用资源
- 能力倾向 - 问答
管道与水箱 - 例题解析
题1 - 两个水管A和B分别可以单独充满一个水箱，A需要24小时，B需要30小时。如果同时打开这两个水管，装满空水箱需要多长时间？
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.
题2 - 一个漏斗可以15小时充满一个水箱。由于底部有一个洞，实际需要20小时才能充满。如果水箱已满，这个洞需要多长时间才能排空？
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
题3 - 漏斗A和B分别可以在6小时和9小时内充满一个水箱，漏斗C可以在12小时内排空。如果同时打开所有三个漏斗，空水箱需要多长时间才能装满？
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.
题4 - 两个水管A和B分别可以在24分钟和32分钟内充满一个水箱。如果同时打开两个水管，那么在多少分钟后关闭水管B，才能使水箱在18分钟内充满？
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.
题5 - 两个水管A和B分别可以在1小时和75分钟内充满一个水箱。还有一个排水管C。如果同时打开三个水管，水箱在50分钟内充满。排水管C排空一个满水箱需要多长时间？
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.
题6 - 两个水管分别可以在14小时和16小时内充满一个水库。同时打开水管，由于底部泄漏，实际需要多花32分钟才能充满水库。水库装满后，泄漏需要多长时间才能排空整个水库？
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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