Question 58·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis
A car uses 5.6 liters of gasoline to travel 100 kilometers on the highway. In city driving, it uses 25% more gasoline per kilometer than on the highway. On a trip, the car travels 80 kilometers on the highway and 50 miles in the city. What is the car's overall fuel efficiency for the entire trip in miles per gallon, rounded to the nearest whole number?
Use:
For multi-part unit-rate problems, split the situation into segments where the rate is constant, compute each segment’s resource use in the same base units, then add. Only after you have totals should you convert to the requested units and form the final rate (total miles divided by total gallons). Keeping units attached at each step helps avoid mixing miles with kilometers or liters with gallons.
Hints
Split the trip into two parts
Handle the highway part and the city part separately, since the city fuel use per kilometer is different.
Be careful with units for each calculation
To find liters used, you need distance in kilometers. To report mpg, you need total distance in miles and total fuel in gallons.
Combine totals at the end
Add the two distances to get total miles, add the two fuel amounts to get total liters (then convert to gallons), and finally compute total miles divided by total gallons.
Desmos Guide
Enter distances and conversions
In Desmos, define highway_km = 80 and city_km = 50*1.609.
Enter fuel-use rates
Type L_per_km_hwy = 5.6/100 and L_per_km_city = L_per_km_hwy*1.25.
Compute total liters and convert to gallons
Type L_total = highway_km*L_per_km_hwy + city_km*L_per_km_city and gal_total = L_total/3.785.
Compute mpg and round
Type miles_total = highway_km/1.609 + 50, then mpg = miles_total/gal_total, then round(mpg) to match the correct choice.
Step-by-step Explanation
Find liters per kilometer for each type of driving
Highway fuel use per kilometer is
City driving uses 25% more per kilometer, so
Convert the city distance to kilometers
Convert 50 miles to kilometers:
Compute total fuel used (liters) for the whole trip
Highway liters:
City liters:
Total liters:
Convert total fuel to gallons
Compute miles per gallon and round
Convert the 80 km highway portion to miles:
Total miles traveled:
Miles per gallon:
Rounded to the nearest whole number, the fuel efficiency is 37.