A certain truck averages 10 miles per gallon GMAT

A certain truck averages 10 miles per gallon when driven in the city and 25 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the truck averages when it is driven 20 miles in the city and 30 miles on the highway?

A. 16

B. 18

C. 20

D. 23

E. 25

This type of question is essentially an average rate question.

We need to figure out how much fuel the truck consumes during its 20 miles in the city and how much fuel it consumes during its 30 miles on the highway. These will be amounts in gallons of fuel.

We can take this information (this number of gallons) and divide by the total number of miles traveled. This will provide us an actual value in miles per gallon.

As you do the calculations, pay special attention to how the units correspond. Multiply each term to cancel out. For example, 10 miles/gal in the city is going to be the same as 1 gal/10 miles.

Let’s start with how much fuel is consumed during the 20 miles in the city. That is:

20 miles * 1/10 gal/mile = 20/10 = 2 gal in the city

Now let’s figure out how much fuel is consumed on the highway. That is:

30 miles * 1/25 gal/mile = 30/25 = 6/5 gal on the highway.

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Now we simply need to add the values to get the total number of gallons. That is:

$2 + \frac{6}{5} = \frac{16}{5} \space gal$

Then we need to divide the total number of miles traveled by this value, which gives an average fuel efficiency in miles/gallon. The total number of miles, of course, is simply 20+30 = 50 miles.

Therefore, the final value will be:

$\frac{50}{\frac{16}{5}} = \frac{250}{16}$