During a certain time period, Car X traveled north along a straight road at a constant rate of 1 mile per minute and used fuel at a constant rate of 5 gallons every 2 hours. During the time period, if Car X used exactly 3.75 gallons of fuel, how many miles did Car X travel?

(A) 36

(B) 37.5

(C) 40

(D) 80

(E) 90

This is a basic distance-rate problem, but the standard D = RT table isn’t very convenient here. Before I jump in, I’m going to do some estimation/approximation and see if I can eliminate some of the answer choices.

First, 1 mile per minute = 60 miles per hour. Second if 5 gallons is equivalent to 2 hours of travel, 3.75 gallons will be more than one hour (it’s more than half of 5 gallons). So, Car X has obviously gone more than 60 miles. A, B, and C are out.

Now if I round 3.75 gallons to 4 gallons, then the corresponding travel time will be 4/5 of 2 hours = 4/5(2) = 8/5 hours. At 60 miles per hour, that’s 60(8/5) miles:

\(\frac{{60}\times{8}}{5} = {12}\times{8} = 96\)

Because I rounded up, this should be slightly larger than the exact distance.

**The correct answer is E.**

If that’s a little bit too seat-of-the-pants for you, we can use a proportion and solve for the exact amount of travel time:

\(\frac{3.75}{5} = \frac{x}{2}\)

\({2}\times{3.75} = 5x\)

And x equals 7.5/5 = 15/10 = 3/2. So 1.5 hours at 60 miles per hour is exactly 90 miles.