A logistics company evaluated three heavy-duty electric cargo vehicles—Truck X, Truck Y, a… — GMAT

A logistics company evaluated three heavy-duty electric cargo vehicles—Truck X, Truck Y, and Truck Z��operating under distinct cargo loads and distances. Match each truck to its corresponding energy consumption rate expressed in kilowatt-hours (kWh) per ton-mile.

- Truck X: Transported a $10$ -ton payload over a distance of $150$ miles, consuming a total of $300$ kWh of energy.
- Truck Y: Transported a $5$ -ton payload over a distance of $200$ miles, consuming a total of $300$ kWh of energy.
- Truck Z: Transported an $8$ -ton payload over a distance of $100$ miles, consuming a total of $400$ kWh of energy.

Truck X ( $10$ -ton payload, $150$ miles, $300$ kWh total) $0.20$ kWh per ton-mile
Truck Y ( $5$ -ton payload, $200$ miles, $300$ kWh total) $0.30$ kWh per ton-mile
Truck Z ( $8$ -ton payload, $100$ miles, $400$ kWh total) $0.50$ kWh per ton-mile

Answer

Truck X matches with

0.20

kWh per ton-mile, Truck Y matches with

0.30

kWh per ton-mile, and Truck Z matches with

0.50

kWh per ton-mile.

To find the rate per ton-mile for each vehicle, calculate total ton-miles by multiplying payload weight by distance, then divide total energy consumption in kWh by total ton-miles. For Truck X:

300 / (10 \times 150) = 0.20

kWh/ton-mile. For Truck Y:

300 / (5 \times 200) = 0.30

kWh/ton-mile. For Truck Z:

400 / (8 \times 100) = 0.50

kWh/ton-mile.

Step-by-Step Solution

Calculate total ton-miles for each vehicle

Truck X:

10 \text{ tons} \times 150 \text{ miles} = 1,500 \text{ ton-miles}

. Truck Y:

5 \text{ tons} \times 200 \text{ miles} = 1,000 \text{ ton-miles}

. Truck Z:

8 \text{ tons} \times 100 \text{ miles} = 800 \text{ ton-miles}

Ton-miles measure total transport work performed (payload mass multiplied by distance).

Compute energy rate per ton-mile for each vehicle

Truck X rate:

\frac{300 \text{ kWh}}{1,500 \text{ ton-miles}} = 0.20 \text{ kWh/ton-mile}

. Truck Y rate:

\frac{300 \text{ kWh}}{1,000 \text{ ton-miles}} = 0.30 \text{ kWh/ton-mile}

. Truck Z rate:

\frac{400 \text{ kWh}}{800 \text{ ton-miles}} = 0.50 \text{ kWh/ton-mile}

Dividing total energy consumed by total ton-miles gives the unit rate per ton-mile.

Map each truck to its matching energy rate

Truck X maps to

0.20

kWh per ton-mile; Truck Y maps to

0.30

kWh per ton-mile; Truck Z maps to

0.50

kWh per ton-mile.

Align each calculated rate with the corresponding item in the right-hand column.

Key Concept

Calculating work-based unit rates (rate = quantity / (payload × distance)).

Estimated Time:1m 30s

Question

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Key Concept

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