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Difficulty: MediumAlgebraic Word Problems and Equation Modeling

A logistics company operates a fleet consisting of standard electric delivery vans and high-capacity electric delivery vans. A standard van consumes a fixed 2.52.5 kilowatt-hours (kWh) of electricity per delivery route, while a high-capacity van consumes 50%50\% more electricity per route than a standard van. On a given day, the fleet completed a total of 4040 delivery routes and consumed a total of 130130 kWh of electricity. How many delivery routes were completed by high-capacity vans?

Answer: 24 routes

Answer

The total number of delivery routes completed by high-capacity vans is 24.
By modeling the relationship using the system S+H=40S + H = 40 and 2.5S+3.75H=1302.5S + 3.75H = 130, substituting S=40−HS = 40 - H gives 100+1.25H=130100 + 1.25H = 130, which resolves to H=24H = 24 high-capacity van routes.

Step-by-Step Solution

1
Calculate the power consumption per route for a high-capacity van.
High-capacity rate = 2.5×1.5=3.752.5 \times 1.5 = 3.75 kWh per route.
High-capacity vans consume 50%50\% more energy than standard vans.
2
Formulate a system of linear equations representing total routes and total electricity used.
S+H=40S + H = 40 and 2.5S+3.75H=1302.5S + 3.75H = 130, where SS represents standard van routes and HH represents high-capacity van routes.
The sum of routes equals 40 and the combined energy consumption equals 130 kWh.
3
Solve for the target variable HH.
Substitute S=40−HS = 40 - H into the energy equation: 2.5(40−H)+3.75H=130  ⟹  100+1.25H=130  ⟹  1.25H=30  ⟹  H=242.5(40 - H) + 3.75H = 130 \implies 100 + 1.25H = 130 \implies 1.25H = 30 \implies H = 24.
Substituting SS yields a single-variable linear equation for HH.

Key Concept

Algebraic Modeling of Systems of Linear Equations
Estimated Time:1m 30s
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Topics

Algebraic Word Problems and Equation Modeling

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