Question is too long so below:

Question

The flow-rate of your current sink faucet is 3 gallons per minute. If you purchase a fancy low-flow faucet for $226, the flow rate would decrease by 32%. Assuming you use your faucet for an average of 1779 minutes per month and water costs $0.007 per gallon, compute the payback period (in months) of such a purchase.

Round your answer to the nearest tenth of a month (tenth place).

Answer 1

The key to this problem is the units. We want to set up a series of fractions and cancel units.

 

(dollars/gallons) •(gallons⁄minutes) • (minutes/months) = dollars/months

 

Right now you pay

 

(0.007) • (3) • (1779) = 37.359 dollars/month

 

If you reduce the flow by 32% you will reduce the number of gallons by 32% and therefore the cost by 32%.

 

32% of 37.359 dollars/month is 11.95488 dollars/month

 

The price of the faucet is 226 dollars and will be paid off in 226 ÷ 11.95488 = 18.9 months