SOLUTION: The reservoir behind Buford Dam can be emptied in 15 days by opening both of its spillways. With the reservoir full, one spillway is opened. Then after 5 days, the second spillwa

Algebra ->  Rate-of-work-word-problems -> SOLUTION: The reservoir behind Buford Dam can be emptied in 15 days by opening both of its spillways. With the reservoir full, one spillway is opened. Then after 5 days, the second spillwa      Log On


   

Question 731548: The reservoir behind Buford Dam can be emptied in 15 days by opening both of its spillways. With the reservoir full, one spillway is opened. Then after 5 days, the second spillway is opened, and the reservoir is then emptied by both spillways in 13 days more. How long would it take each spillway alone to empty the reservoir?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
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%2A5 = how much of the job is done for the first five days.
%28h%2Bk%29%2A13 = 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%28h%2A5%2B%28h%2Bk%29%2A13=1%29.

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%2F15=h%2Bk or highlight%28h%2Bk=1%2F15%29.

The system in crude form to solve is this:
highlight%28h%2A5%2B%28h%2Bk%29%2A13=1%29
AND
highlight%28h%2Bk=1%2F15%29
Solve for h and k.