Answer:
Let's denote the average rate of evaporation in the pool as R gallons per hour.
The rate of evaporation in the shade is given as 6 gallons per hour, and the rate in the sun is given as 19 gallons per hour. We are told that the amount of water lost in the shade is equal to the amount lost in the sun during these weeks in August.
So, we can set up the following equation:
Rate of evaporation in shade (6 gal/hr) * Time in shade (hours) = Rate of evaporation in sun (19 gal/hr) * Time in sun (hours)
Let's say the time in the shade is t hours, and the time in the sun is also t hours.
6 * t = 19 * t
Now, we can solve for t:
19t - 6t = 0
13t = 0
t = 0
Wait, something doesn't seem right. The equation implies that t is 0, which means there was no time spent in either the shade or the sun, which is not possible. This implies there may be an error in the provided information or question.
If there was a typo or an omission in the question, please provide the correct or complete information so that I can assist you further.