Dimensional Analysis Problem Help

Question

A car travels at 55 miles/hour and gets 8 miles.liters of gasoline for fuel economy. How many gallons of gasoline are needed for a 3.0 hour trip? Provide your answer in the correct number of significant figures.

4 quarts = 1 gallon, 12 inches = 1 foot, 2.54 cm = inch, 5280 feet = 1 mile, 1 liter = 1.057 quarts.

Answer 1

5.45 gallons are needed for the 3 hour trip

55 mph for a 3 hour trip means 3x55=165 mile trip.

You seem to have 8 miles per liter. that means you need 165/8 liters or 20 5/8 liters = 20.625 liters

convert that to quarts and then to gallons. each liter = 1.057 quarts. So, 20.625 x 1.057 quarts is needed = 21.801 quarts

Divide by 4 to get the number of gallons needed, 21.801/4 = 5.450 gallons for a 3 hour trip, going 165 miles

check the answer

8 miles per liter means 8/0.2642 miles per gallon or 30.280 miles per gallon, which is a reasonable mpg 1 liter is 0.2642 gallons

30.280 x 5.450 = 165.026 miles, slight rounding error making it almost the required 165.000 miles