Officials begin to release water from a full man-made lake at a rate that would empty the lake in 16 weeks, but a river that can fill the lake in 25 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.

400/9 weeks to empty the lake

Step-by-step explanation:

Let t = the time to empty the lake

The rate of water being released = 1/16

The rate of water being replenished = 1/25

rate times time = amount of work done

1/16(t) = the amount water that is being released

1/25(t) = the amount of water the river is putting into the lake

amount being released - amount being replenished = 1 empty lake

t/16 - t/25 = 1

25t - 16t = 16(25)

9t = 16(25)

t = 16(25)/9 =  400/9 weeks to empty the lake

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answer:

step-by-step explanation: