[tex]\dfrac{1}{22}\:\dfrac{\text{in}}{\text{hr}}[/tex]
Step-by-step explanation:
The amount of time from 10pm to 7am is 9 hours. However, the time indicated is 7:10am. Since there are 60 minutes in an hour, 10 min is equal to 1/6 of an hour. Therefore, the total time that the water level of the pool decreased is [tex]9\frac{1}{6}[/tex] hours or [tex]\frac{55}{6}[/tex] hours. To find the rate at which the water level decreased, we divide the change in the water (in inches) by the time it took to reach that level. So we write
rate of change [tex]= \dfrac{\text{change\:in\:height}}{\text{change\:in\:time}}[/tex]
[tex]\:\:\:\:\:\:\:= \dfrac{\frac{5}{12}\:\text{in}}{\frac{55}{6}\:\text{hrs}}[/tex]
[tex]\:\:\:\:\:\:\:=\dfrac{5}{12}\cdot\dfrac{6}{55}\:\dfrac{\text{in}}{\text{hr}}[/tex]
[tex]\:\:\:\:\:\:\:= \frac{1}{22}\:\dfrac{\text{in}}{\text{hr}}[/tex]
