Question

Officials begin to release water from a full man-made lake at a rate that would empty the lake in 4 weeks, but a river that can fill the lake in 15 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.

Answer 1

Answer:

5 weeks and 5 days is required to empty the lake

Explanation:

Officials begin the remove water from a full man made lake

The lake can be emptied in 4 weeks

= -1/4

A river can fill the lake up in 15 weeks

= 1/15

Let t represent the number of weeks that is required to empty the lake

= -1/t

Therefore the number of weeks it takes to empty the lake can be calculated as follows

-1/t= -1/4 + 1/15

-1/t= -11/60

Cross multiply

-11×t= -1×60

-11t= -60

t = 60/11

t= 5 5/11

Hence it takes 5 weeks and 5 days to empty the lake