The house Trevor's family lives in has $6$ people (including Trevor) and $3$ bathrooms. In the past month, each person showered for an average of $480$ minutes and used an average $72$ liters of shower water (over the entire month). Water costs $0.20$ dollars per liter. $\newline$ How much did Trevor's family pay per minute on shower water?

Full solution

Q. The house Trevor's family lives in has

6

people (including Trevor) and

3

bathrooms. In the past month, each person showered for an average of

480

minutes and used an average

72

liters of shower water (over the entire month). Water costs

0.20

dollars per liter.

\newline

How much did Trevor's family pay per minute on shower water?

Calculate total water usage: First, calculate the total amount of water used by Trevor's family for showering in the past month. Since there are $6$ people and each used an average of $72$ liters, we multiply the number of people by the average liters used per person. $\newline$ Calculation: $6$ people $\times$ $72$ liters/person $=$ $432$ liters
Calculate total cost of water: Next, calculate the total cost of the water used by Trevor's family for showering. Since water costs $0.20$ dollars per liter, we multiply the total liters used by the cost per liter. $\newline$ Calculation: $432 \, \text{liters} \times 0.20 \, \text{dollars/liter} = 86.4 \, \text{dollars}$
Calculate total showering time: Now, calculate the total minutes spent showering by Trevor's family in the past month. Since each person showered for an average of $480$ minutes, we multiply the number of people by the average minutes spent showering per person. $\newline$ Calculation: $6$ people $\times$ $480$ minutes/person $= 2880$ minutes
Calculate cost per minute: Finally, calculate the cost per minute for shower water. We divide the total cost of the water by the total minutes spent showering. $\newline$ Calculation: $\frac{86.4 \text{ dollars}}{2880 \text{ minutes}} = 0.03 \text{ dollars/minute}$