Question 1184052
rate * time = quantity.


you have 1 lake, so quantity = 1.


formula becomes rate * time = 1


it takes 16 weeks to empty the lake.
rate * 16 = 1
rate = 1/16
this means 1/16 of the lake is empties each week.


it takes 25 weeks to fill up the lake.
rate * 25 = 1
rate = 1/25
this means 1/25 of the lake is replenished each week.


every week, 1/16 week of the lake is removed and 1/25 of the lake is replenished.
the net loss each week is 1/16 - 1/25 = 25/400 - 16/400 = 9/400 of the lake.


if you start with a full lake and have a net loss of 9/400 of the lake each week, the formula of rate * time = quantity becomes 9/400 * time = 1
solve for time to get:
time = 400/9 weeks.


the lake will be empty in 400/9 weeks.


in that time, the amount of lake that is removed is 1/16 * 400/9 = 25/9 times the original amount of the lake.


in that time, the amount of lake that is replenished is 1/25 * 400/9 = 16/9 times the original amount of the lake.


the net amount of lake that is removed in 400/9 weeks is 25/9 - 16/9 = 9/9 = 1 times the mount of water in the lake.


this confirms the solution is correct.


the solution is that it takes 400/9 weeks to empty the lake.