Question

for each situation, find the unit rates. then, choose a unit rate to solve the problem in part c. show your reasoning. 1 a laundry service uses 10 gallons of detergent every 6 weeks. a. how many gallons of detergent does the laundry service use per week? b. how many weeks does it take the laundry service to use 1 gallon of detergent? c. how many weeks will it take the laundry service to finish 3 gallons of detergent?

Explanation:

Step1: Find gallons per week

To find the number of gallons of detergent used per week, divide the total gallons by the total weeks. The laundry service uses 10 gallons in 6 weeks. So the unit - rate of gallons per week is $\frac{10}{6}=\frac{5}{3}$ gallons per week.

Step2: Find weeks per gallon

To find the number of weeks it takes to use 1 gallon of detergent, divide the total weeks by the total gallons. Since it takes 6 weeks to use 10 gallons, the unit - rate of weeks per gallon is $\frac{6}{10}=\frac{3}{5}$ weeks per gallon.

Step3: Solve for part c

To find the number of weeks it takes to use 3 gallons of detergent, use the weeks - per - gallon unit rate. Multiply the number of gallons (3) by the weeks per gallon ($\frac{3}{5}$). So the number of weeks is $3\times\frac{3}{5}=\frac{9}{5} = 1.8$ weeks.

Answer:

a. $\frac{5}{3}$ gallons per week
b. $\frac{3}{5}$ weeks per gallon
c. 1.8 weeks