SOLUTION: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 6 weeks, but a river that can fill the lake in 20 weeks is replenishing the lake a

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 6 weeks, but a river that can fill the lake in 20 weeks is replenishing the lake a      Log On


   

Question 949827: Officials begin to release water from a full man-made lake at a rate that would empty the lake in 6 weeks, but a river that can fill the lake in 20 weeks is replenishing the lake at the same time. How long does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.
Found 2 solutions by josgarithmetic, macston:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform fill or work rates, using the lake as the unit of volume, for 1 LAKE.
Time is quantity of weeks. Notice the filling rate uses less time than the emptying rate. The rate for both together is the sum of the individual rates. Understand that the two rates are of opposite signs.

1%2F6-1%2F20, LAKES per WEEK.

You are finally interested in the reciprocal of that. How many weeks.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Lake empties at rate -1 lake/6wks=-1/6 lake/wk
Lake fills at rate lake/20wks=1/20 lake/wk
Combined rate: -1/6 lake/wk + 1/20 lake/wk=-10/60 lake/wk +3/60 lake/wk=-7/60 lake/wk
To empty the 1 lake at rate -7/60 lake/wk=1/(-7/60)=-(60/7)wks= 8 4/7 wks
ANSWER: It would take 8 weeks and 4 days to empty the lake.