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Difficulty: MediumRatios, Rates, and Proportions

An electric commuter train consumes energy at a constant rate of 450 kilowatt-hours (kWh)450\text{ kilowatt-hours (kWh)} for every 120 miles120\text{ miles} it travels. Electricity costs $0.14\$0.14 per kWh\text{kWh}. What is the total cost of the electricity consumed by the train during a 320 mile320\text{ mile} trip?

  1. A
    $23.63\$23.63
  2. B
    $63.00\$63.00
  3. $168.00\$168.00Answer
  4. D
    $448.00\$448.00
  5. E
    $1,200.00\$1,200.00

Answer

The total cost of electricity consumed during the trip is $168.00\$168.00.
To solve this problem, first determine the energy consumed per mile by dividing 450 kWh450\text{ kWh} by 120 miles120\text{ miles}, which equals 3.75 kWh/mile3.75\text{ kWh/mile}. Next, multiply this unit rate by 320 miles320\text{ miles} to find the total energy required for the trip, which is 1,200 kWh1,200\text{ kWh}. Finally, multiply 1,200 kWh1,200\text{ kWh} by the cost of $0.14\$0.14 per kWh\text{kWh} to get the total cost of $168.00\$168.00.

Step-by-Step Solution

1
Calculate the unit rate of energy consumption per mile
450 kWh120 miles=3.75 kWh per mile\frac{450\text{ kWh}}{120\text{ miles}} = 3.75\text{ kWh per mile}
Determining the energy consumption rate per mile allows us to calculate energy used for any distance.
2
Find the total energy consumed for 320320 miles
320 miles×3.75 kWh/mile=1,200 kWh320\text{ miles} \times 3.75\text{ kWh/mile} = 1,200\text{ kWh}
Multiply total distance by rate per mile to find total electricity required.
3
Calculate the total electricity cost
1,200 kWh×$0.14/kWh=$168.001,200\text{ kWh} \times \$0.14\text{/kWh} = \$168.00
Multiply total kilowatt-hours by the cost per kilowatt-hour.

Key Concept

Unit rates and multi-step proportional reasoning
Estimated Time:1m 30s
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Topics

Ratios, Rates, and Proportions

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