Question 1074980
.
<pre>
Let x = time in hours for the faster pipe to fill the tank alone.
Then the time for the other pipe is (x+5) hours.

The faster pipe fills {{{1/x}}} of the tank volume per hour.
The slower pipe fills {{{1/(x+5)}}} of the tank volume per hour.

Working together, they fill {{{1/x + 1/(x+5)}}} of the tank volume per hour.

According to the condition,

{{{1/x + 1/(x+5)}}} = {{{1/5}}}.

It is your equation to solve.
The first step is to multiply both sides by 5x*(x+5). You will get

5(x+5) + 5x = x*(x+5),   or

5x + 25 + 5x = x^2 + 5x,

x^2 - 5x - 25 = 0.

{{{x[1,2]}}} = {{{(5 +- sqrt (25 + 4*25))/2}}} = {{{(5 +- 5*sqrt(5))/2}}}.

{{{x[1]}}} = {{{(5 + 5*sqrt(5))/2}}} = 8.1 hours (approximately).

The second root is negative and doesn't work.


<U>Check</U>.  {{{1/8.1 + 1/(8.1+5)}}} = 0.2.  Correct !


<U>Answer</U>. Faster pipe in 8.1 hours. Slower pipe in 13.1 hours.
</pre>

Solved.


For a wide variety of similar solved joint-work problems with detailed explanations see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using Fractions to solve word problems on joint work</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Solving-more-complicated-word-problems-on-joint-work.lesson>Solving more complicated word problems on joint work</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Selected-problems-from-the-archive-on-joint-work-word-problems.lesson>Selected joint-work word problems from the archive</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Using-quadr-eqns-to-solve-word-problems-on-joint-work.lesson>Using quadratic equations to solve word problems on joint work</A> (*)

in this site.


Read them and get be trained in solving joint-work problems.


Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this textbook under the topic "<U>Rate of work and joint work problems</U>" of the section "<U>Word problems</U>".



The lesson in the list marked by (*) contains other similar solved problems relevant to yours.