Question 731548
The rate of each spillway are unknown.  Let h = rate for "one" spillway and k = rate for the "second" spillway.  The units for these rates are as "empty the reservoir per day".  


The task completion equation is r*t=j, r stands for rate, t stands for days, j stands for job or task, which is "emptying the reservoir".  The situation starts with the reservoir being full.


These are the time periods.
{{{h*5}}} = how much of the job is done for the first five days.
{{{(h+k)*13}}} = how much of the job is done for the thirteen days during which both spillways are open.  The sum of those expressions is equal to the WHOLE job.
{{{highlight(h*5+(h+k)*13=1)}}}.


The beginning of the problem description gives us h+k information.  ONE job is done in 15 days when both spillways are open at the same time.  That is, {{{1/15=h+k}}} or {{{highlight(h+k=1/15)}}}.


The system in crude form to solve is this:
{{{highlight(h*5+(h+k)*13=1)}}}
AND
{{{highlight(h+k=1/15)}}}
Solve for h and k.