# Math Help - Quadratic Equations

Hi,

I am stuck on this questions:

A certain tank can be filled by two pipes in 80 minutes. The larger pipe by itself can fill the tank in 2 hours less than the small pipe by itself. How long does each pipe take to fill the tank on it's own?

My attempt so far:

Large pipe = l
Small pipe = s
time = t

Hence:
(Large pipe + Small pipe) x time = 1 filled tank

$(l + s)80 = 1$

$lt = st - 120$

$st-lt=120$

$t(s-l) 120$

Since $l = (1 - 80s) / 80$

$t(s-((1-80s)/80))=120$

$t(160s-1) = 120*80$

I still have the s in the answer? how am i suppose to calculate t?

2. What exactly do you mean by Large pipe = l? Is l the time the large pipe takes to fill the tank? In what, minutes, hours? Is it the portion of the tank that gets filled after one hour with the large pipe running? What is it?

I suggest the following: let

l = the time the large pipe takes to fill the tank, in minutes
s = the time the small pipe takes to fill the tank, in minutes

The large pipe being able to fill the tank in 2 hours less than the small one immediately gives $s=l+120$ (remember we are working in minutes, so 2h = 120mins). To get the second condition, think of it as follows: if the large pipe takes l minutes to fill the tank, then (assuming they pour water at constant rate) it will fill $\frac{1}{l}$ of the tank in a single minute. So in 80 minutes, it will fill $\frac{80}{l}$ of the tank. Same goes for s, and you finally get:

$\frac{80}{s}+\frac{80}{l}=1$ (1 being one filled tank)

Try to work these out now, and you'll see a quadratic equation appearing along the way, which may explain your thread title

3. I have done as advised. However i am not getting the correct answer?

So we have two equations:

$\frac {8}{L} + \frac {8}{S} = 1$

$S = L + 120$

$\frac {80}{L} + \frac{80}{L+80} = 1$

$(L+ 80) 80 + 80L = L(L+80)$

$80L + 80*80 + 80L = L^2+80L$

$L^2-80L-6400 = 0$

Applying the quadratic formula we have

$L = \frac {80 + \sqrt {32000}}{2}$

Which is not the correct answer. The answer as given in the textbook is Large pipe 2 hours , small pipe 4 hours?

4. Originally Posted by M.R
I have done as advised. However i am not getting the correct answer?

So we have two equations:

$\frac {8}{L} + \frac {8}{S} = 1$

$S = L + 120$

$\frac {80}{L} + \frac{80}{L+80} = 1$ Mr F says: This line is wrong (and all that follows will be wrong). It should be ${\color{red}\frac {80}{L} + \frac{80}{L+{\color{blue}120}} = 1}$.

$(L+ 80) 80 + 80L = L(L+80)$

$80L + 80*80 + 80L = L^2+80L$

$L^2-80L-6400 = 0$

Applying the quadratic formula we have

$L = \frac {80 + \sqrt {32000}}{2}$

Which is not the correct answer. The answer as given in the textbook is Large pipe 2 hours , small pipe 4 hours?
..

5. Sorry for the late reply. Thank you very much for all your help guys, i worked it out.