Question 1136589
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<pre>

Let " t " be the time for old boiler to burn the load coal (in "days").

Then the time for new boiler to burn the load coal will be (t+5) days.



Thus the rate of burning for the old boiler is  {{{1/t}}}  of the total load per day;

     the rate of burning for the new boiler is  {{{1/(t+5)}}}  of the total load per day.



When the two boilers work simultaneously, their combined rate is the sum  {{{1/t}}} + {{{1/(t+5)}}},

and it is equal to  {{{1/6}}},  according to the condition.


So, your equation is


    {{{1/t}}} + {{{1/(t+5)}}} = {{{1/6}}}.



To solve it, first multiply both sides by 6t*(t+5); then simplify


    6*(t+5) + 6t = t*(t+5)

    6t + 30 + 6t = t^2 +5t

    t^2 - 7t -30 = 0

    (t-10)*(t+3) = 0


Only positive root  t = 10 days is meaningful.


<U>Answer</U>.  10 days for old boiler and 15 days for new boiler.


<U>CHECK</U>.    {{{1/10}}} + {{{1/15}}} = {{{3/30 + 2/30}}} = {{{5/30}}} = {{{1/6}}}.   ! Correct !
</pre>

Solved.


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It is a standard and typical joint work problem.


There is a wide variety of similar solved joint-work problems with detailed explanations in this site. &nbsp;See the lesson

&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> 



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


Also, &nbsp;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 lesson is the part of this textbook under the topic 
"<U>Rate of work and joint work problems</U>" &nbsp;of the section &nbsp;"<U>Word problems</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.