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Question

Difficulty: MediumDirect Proportions

A military supply convoy consumes 2424 gallons of diesel fuel to travel 140140 miles. Assuming the fuel consumption rate remains constant, how many gallons of diesel fuel are required for the convoy to travel a distance of 315315 miles?

Answer: 54 gallons

Answer

54
By setting up a direct proportion between the distance traveled and the fuel consumed (14024=315x\frac{140}{24} = \frac{315}{x}) and cross-multiplying, we solve for xx and determine that the convoy requires exactly 5454 gallons of fuel.

Step-by-Step Solution

1
Set up a direct proportion relating distance to fuel consumption.
14024=315x\frac{140}{24} = \frac{315}{x}
Since the fuel consumption rate is constant, the ratio of miles traveled to gallons consumed remains the same.
2
Cross-multiply the proportion.
140x=24×315140x = 24 \times 315
Cross-multiplication converts the proportion into a linear equation to solve for the unknown variable xx.
3
Simplify the right side of the equation.
140x=7560140x = 7560
Multiplying the known values prepares the equation for the final isolation step.
4
Divide by 140140 to solve for xx.
x=7560140=54x = \frac{7560}{140} = 54
Dividing both sides by 140140 isolates xx, revealing the required gallons of fuel.

Key Concept

Direct Proportions
Estimated Time:1m 0s
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Topics

Direct Proportions

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