The Cobb family of Fremont is looking at ways to decrease their home water and energy usage. Their current electric hot-water heater raises the water temperature to 140 degree F, which requires 0.20 kWh/gallon at a cost of $0.10/kWh. Each person in the family of four showers once a day for an average of 10 minutes per shower. The shower has a flow rate of 5.0 gallons per minute. a. Calculate the following. Be sure to show all your work and include units with your answers. i) The total amount of water that the family uses per year for taking showers. ii) The annual cost of the electricity for the family showers, assuming that 2.5 gallons per minute of the water used is from the hot-water heater b. The family is considering replacing their current hot-water heater with a new energy-efficient hot-water heater that costs $1,000 and uses half the energy that their current hot-water heater uses. How many days would it take for the new hot-water heater to recover the $1,000 initial cost?

Question

Roberto Gregory

Mathematics

23 August, 07:07

The Cobb family of Fremont is looking at ways to decrease their home water and energy usage. Their current electric hot-water heater raises the water temperature to 140 degree F, which requires 0.20 kWh/gallon at a cost of $0.10/kWh. Each person in the family of four showers once a day for an average of 10 minutes per shower. The shower has a flow rate of 5.0 gallons per minute. a. Calculate the following. Be sure to show all your work and include units with your answers. i) The total amount of water that the family uses per year for taking showers. ii) The annual cost of the electricity for the family showers, assuming that 2.5 gallons per minute of the water used is from the hot-water heater b. The family is considering replacing their current hot-water heater with a new energy-efficient hot-water heater that costs $1,000 and uses half the energy that their current hot-water heater uses. How many days would it take for the new hot-water heater to recover the $1,000 initial cost?

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Answers (1)

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Paul Boyd · Answer 1

ai) 73000 gal/yr

aii) $730 per year

b) 1000 days

Step-by-step explanation:

ai) The water usage per day is ...

(4 showers/day) (10 min/shower) (5 gal/min) = 200 gal/day

Then the usage per year is ...

(200 gal/day) (365 days/yr) = 73,000 gal/yr

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aii) The cost of electricity is the cost of heating half the water usage, so is ...

(0.20 kWh/gal) (1/2) (73,000 gal/yr) ($0.10/kWh) = $730/yr

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b) The current daily cost of electricity for heating water is ...

($730/yr) / (365 days/yr) = $2/day

If the cost is cut in half, it will be $1 per day. That means the savings is $1 per day, so it will take 1000 days to recover the $1000 initial cost. (Effectively, the average cost for the first 1000 days is the same as if the water heater had not been replaced.)