SOLUTION: A small pipe fills a water tank in x minutes, whereas a larger pipe fills the same tank in (x-8) minutes. (a) Write down an expression, in terms of x, for the fraction of the t

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Question 789284: A small pipe fills a water tank in x minutes, whereas a larger pipe fills the same tank in (x-8) minutes.
(a) Write down an expression, in terms of x, for the fraction of the tank filled with water in one minute using
(i) the small pipe
(ii) the large pipe
If both pipes are used together, the tank can be filled in 7.5 minutes.
(b) Form an equation involving x and show that it reduces to x^2-23x+60=0
(c) Solve the equation x^2-23x+60=0
(d) Hence, find the time taken to fill the tank using only the large pipe.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
(a)
With just small pipe:
Rate of filling is ( 1 tank ) / ( x min )
Multiply by ( 1 min ) to get fraction
of tank filled in min

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With just large pipe:

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(b)

Multiply both sides by

Use the quadratic formula

and, also,

The answer can't be because cannot be
subtracted from it to get a positive number
So, min
and

The large pipe fills the tank in 12 min