A car travels 120.5 miles on 3.5 gallons of gas. If the car's fuel efficiency remains constant, how many miles can it travel on 10 gallons of gas?

To solve this problem, we need to determine the car's fuel efficiency in miles per gallon (mpg) and then use that to find out how many miles it can travel on 10 gallons of gas. ### Step 1: Calculate the fuel efficiency The fuel efficiency (mpg) can be calculated using the formula: \[ \text{Fuel Efficiency} = \frac{\text{Distance}}{\text{Gallons of Gas}} \] Given: - Distance = 120.5 miles - Gallons of Gas = 3.5 gallons Substituting the values into the formula: \[ \text{Fuel Efficiency} = \frac{120.5}{3.5} \] ### Step 2: Calculate the distance for 10 gallons Once we have the fuel efficiency, we can calculate the distance the car can travel on 10 gallons of gas using the formula: \[ \text{Distance} = \text{Fuel Efficiency} \times \text{Gallons of Gas} \] Substituting the values: \[ \text{Distance} = \text{Fuel Efficiency} \times 10 \] Now, let's perform the calculations. First, we will calculate the fuel efficiency. Calculate the value by following steps: - step0: Calculate: \(\frac{120.5}{3.5}\) - step1: Convert the expressions: \(\frac{\frac{241}{2}}{\frac{7}{2}}\) - step2: Multiply by the reciprocal: \(\frac{241}{2}\times \frac{2}{7}\) - step3: Reduce the numbers: \(241\times \frac{1}{7}\) - step4: Multiply: \(\frac{241}{7}\) Calculate or simplify the expression \( 34.428571 \). Numbers by following steps: - step0: Solution: \(34.428571\) Calculate or simplify the expression \( 34.428571 * 10 \). Calculate the value by following steps: - step0: Calculate: \(34.428571\times 10\) - step1: Multiply the numbers: \(344.28571\) ### Step 1: Calculate the fuel efficiency The fuel efficiency of the car is approximately: \[ \text{Fuel Efficiency} \approx 34.43 \text{ miles per gallon} \] ### Step 2: Calculate the distance for 10 gallons Using the fuel efficiency, we can calculate the distance the car can travel on 10 gallons of gas: \[ \text{Distance} = 34.43 \times 10 \approx 344.29 \text{ miles} \] ### Final Answer The car can travel approximately **344.29 miles** on 10 gallons of gas.