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    of the total load per day;

     the rate of burning for the new boiler is    of the total load per day.



When the two boilers work simultaneously, their combined rate is the sum   + ,

and it is equal to  ,  according to the condition.


So, your equation is


     +  = .



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.


Answer.  10 days for old boiler and 15 days for new boiler.


CHECK.     +  =  =  = .   ! Correct !