Bunuel wrote:
A certain car can travel 48 kilometers on a liter of fuel. If the fuel tank’s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed, how fast is the car moving, in miles per hour? (1 gallon = 3.8 liters; 1 mile = 1.6 kilometers)
A. 52
B. 65
C. 78
D. 91
E. 104
Kudos for a correct solution.
MANHATTAN GMAT OFFICIAL SOLUTION:This problem is all about quick but careful unit conversion. One fast but safe way to convert units is to use conversion factors, which are essentially fractions with equivalent amounts on top and bottom (but different units). As you multiply conversion factors together, you cancel units, in the same way as you cancel common factors from numerators and denominators.
Start with kilometers per liter:
48 km / liter
You ultimately want to get to miles per hour, or miles / hour. So we need to eliminate kilometers from the numerator and replace it with miles. We can do so by multiplying by this conversion factor:
1 mile / 1.6 km
We get this:
(48 km / liter)(1 mile / 1.6 km) = 48/1.6 miles per liter
We can cancel numeric factors now, or we can wait. Since 1.6 is just a decimal point move away from 16, which goes into 48, let’s go ahead and cancel:
48/1.6 = 480/16 = 30 miles per liter
Now, let’s get rid of liters, converting to gallons in the denominator:
(30 miles / liter)(3.8 liters / 1 gallon) = (30 × 3.8) miles per gallon
Save the full computation for now, but a quick & easy move is to trade decimal points:
(30 × 3.8) miles per gallon = (3 × 38) miles per gallon
Finally, let’s “convert” gallons to hours. These two units measure very different things (volume and time), but we have an effective conversion between them: the car uses up 3.9 gallons over a period of 5.7 hours, so the rate of converting between gallons and hours for this trip is 3.9 gallons per 5.7 hours.
(3 × 38 miles / gallon)(3.9 gallons / 5.7 hours) = (3 × 38 × 3.9 / 5.7) miles per hour
Now we just need to simplify the fraction. Use decimal moves again:
3 × 38 × 3.9 / 5.7 = 3 × 38 × 39 / 57
38 = 2 × 19 and 57 = 3 × 19, so cancel out a common factor of 19:
3 × 38 × 39 / 57 = 3 × 2 × 39 / 3 = 2 × 39 = 78
The correct answer is C.
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