Form 4 Chapter 2 Quadratic Equations 01

有位学生在网上论坛提出这道数学题，寻求帮助。我看了一看，心里也“痒”了，就尝试回答这道问题。我把解答步骤贴在此，希望有兴趣的学生也可从此网站学习高级数学。

A rectangular tank can be filled with water by 2 pipes in 6 minutes. If the larger pipe alone takes 5 minutes less to fill the tank than the smaller pipe, find the possible time each pipe will take to fill the tank. (Hint: use the concept of rate of flow.)



V = volume of tank

T = time for smaller pipe to fill the tank

L = rate of flow for larger pipe

S = rate of flow for smaller pipe

A rectangular tank can be filled with water by 2 pipes in 6 minutes:

V = (L+S) X 6

V = 6V + 6S ——– (1)

If the larger pipe alone takes 5 minutes less to fill the tank than the smaller pipe:

V = ST

S = V/T——– (2)

V = L(T-5)

L = V/(T-5) ——- (3)

Substitute (2) and (3) into (1)

V = 6V/(T-5) + 6V/T

Divide by V

1 = 6/(T-5) + 6/T

1-6/T = 6/(T-5)

(T-6)/T = 6/(T-5)

(T-6)(T-5) = 6T

T^2-11T+30 = 6T

T^2-17T+30 = 0

(T-15)(T-2) = 0

T = 15 or T = 2

because T>5, therefore T = 15.

Therefore, time for smaller pipe is 15 minutes and time for larger pipe is 10 minutes.