Sure, let's break down the solution step-by-step to determine who can drive farther on 40 gallons of gasoline, Lauren or Melissa.
### Step 1: Calculate Miles Per Gallon
First, we must find out how many miles each person can drive per gallon of gasoline.
#### Lauren's Car:
Lauren can drive 320 miles on 10 gallons of gasoline. To find out how many miles she can drive per gallon, we divide the total miles by the number of gallons:
[tex]\[ \text{Miles per gallon for Lauren} = \frac{320 \text{ miles}}{10 \text{ gallons}} = 32 \text{ miles per gallon} \][/tex]
#### Melissa's Car:
Melissa can drive 280 miles on 8 gallons of gasoline. To find out how many miles she can drive per gallon, we divide the total miles by the number of gallons:
[tex]\[ \text{Miles per gallon for Melissa} = \frac{280 \text{ miles}}{8 \text{ gallons}} = 35 \text{ miles per gallon} \][/tex]
### Step 2: Calculate Distance Covered on 40 Gallons
Next, we need to determine how far each person can drive on 40 gallons of gasoline. We do this by multiplying their miles per gallon by 40 gallons.
#### Lauren's Car:
[tex]\[ \text{Distance on 40 gallons for Lauren} = 32 \text{ miles per gallon} \times 40 \text{ gallons} = 1280 \text{ miles} \][/tex]
#### Melissa's Car:
[tex]\[ \text{Distance on 40 gallons for Melissa} = 35 \text{ miles per gallon} \times 40 \text{ gallons} = 1400 \text{ miles} \][/tex]
### Conclusion
Lauren can drive 1280 miles on 40 gallons of gasoline, whereas Melissa can drive 1400 miles on the same amount.
Thus, Melissa can drive farther on 40 gallons of gasoline.
