A easy math question.

[匿名]

2010-11-12 4:14 pm

An upright cylindrical measuring cylinder is filled with water to n cm high, where
n >12 . It is known that if holes are drilled on the cylinder, water will flow away
from the hole at a constant rate as long as the water level is above the hole. The
flow rates in all holes are equal. When one hole is drilled each at the base, 5 cm
high and 12 cm high, all water will flow away in 5 minutes. When one hole is
drilled each at the base, 5 cm high, 9 cm high and 12 cm high, all water will flow
away in 4 minutes. Find the value of n.

回答 (1)

用戶2053

2010-11-12 11:51 pm

✔ 最佳答案

[ n------12---------9-------------5---------------0 ]
Let S cm per minute be the flowing speed of each hole , then :(n - 12)/(3S) + (12 - 5)/(2S) + 5/S = 52(n - 12) + 21 + 30 = 30S2n + 27 = 30S ...........(1)
(n - 12)/(4S) + (12 - 9)/(3S) + (9 - 5)/(2S) + 5/S = 43(n - 12) + 12 + 24 + 60 = 48Sn + 20 = 16S .............(2)(2)*2 - (1) :40 - 27 = 2S
S = 6.5 , subs into (2) :n = 84

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