Miles, Gallons, and Math: Mastering Fuel Efficiency Questions

Question

How many times while driving your vehicle on a long trip, or while refuelling have you thought about the miles you will be able to cover with the amount of fuel you have in your vehicle? Quite often, yeah? If not, GMAT would want you to think about it.

Alright, let’s talk about a specific type of GMAT Quant problem - fuel consumption rates. These problems might seem tricky at first, but once you see the underlying pattern, they become much easier to handle.

Two Types of Rates

Imagine you’re driving a car or piloting a boat. There are two rates involved:

Speed  – how fast the vehicle is moving (miles per hour or kilometers per hour). 
  Fuel Consumption Rate  – how much fuel is used (either in gallons per mile or gallons per hour).

Why is This Important?

The challenge in these problems is that sometimes fuel consumption is given per unit of  distance  (like miles per gallon), and sometimes it's given per unit of  time  (like gallons per hour). You need to know how to switch between these two formats.

MPG  (miles per gallon): For every gallon of fuel used, the vehicle can travel a certain number of miles. For example, if a car has a fuel efficiency of 30 MPG, then it can travel 30 miles using one gallon of fuel. 
  GPH  (gallons per hour): the vehicle consumes a certain number of gallons for every hour of operation. For instance, if a boat burns fuel at a rate of 10 GPH, it means that every hour, the boat uses up 10 gallons of fuel,  regardless of how far it travels .

How Do You Switch Between These Rates?

Simple! Look for the  common unit  between speed and fuel consumption. Since speed is always in distance/time, you can use it as a bridge between fuel per mile and fuel per hour.

Quick example! Imagine a truck consumes fuel at a rate of 8 gallons per hour and travels at a speed of 40 miles per hour. How many miles does it travel per gallon?

In 1 hour, it covers  40 miles  and consumes  8 gallons . 
 To find miles per gallon:  40 miles / 8 gallons = 5 miles per gallon .

The key is to get better at translation, and have flexibility translating and manipulating units.

Relationship Between Speed, MPG, and GPH

Speed (MPH)  = Distance / Time 
  Miles per gallon (MPG)  = Speed (MPH) ÷ Fuel consumption (GPH) 
  Gallons per hour (GPH)  = Speed (MPH) ÷ Miles per gallon (MPG)

Let’s dive into examples and start taking on some real GMAT questions:

While traveling at a constant speed of 32 miles per hour, a certain motorboat consumes 24 gallons of fuel per hour. What is the fuel consumption of this boat at this speed measured in miles traveled per gallon of fuel?

(A) 2/3 
 (B) 3/4 
 (C) 4/5 
 (D) 4/3 
 (E) 3/2

Step 1: Identify Given Information

Speed =  32 miles per hour  
 Fuel consumption =  24 gallons per hour

Step 2: Match the Common Unit

Since both rates use  hours , we can directly compare:

In 1 hour, the boat travels  32 miles  and uses  24 gallons . 
 That means in  32 miles , it consumes  24 gallons . 
 We want miles per gallon, so let’s divide:  32 miles / 24 gallons = 4/3 miles per gallon

The correct answer is  4/3 (D).

This question is discussed  here.

Another Example with More Steps

Let's look at a car problem:

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 this 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

Step 1: Convert Speed into a More Useful Form

The car travels  1 mile per minute , which is  60 miles per hour . 
 Fuel consumption =  5 gallons per 2 hours , so let’s express that per hour:  5 gallons / 2 hours = 2.5 gallons per hour

Step 2: Find Miles per Gallon

Speed =  60 miles per hour  
 Fuel use =  2.5 gallons per hour  
 Miles per gallon =  60 miles / 2.5 gallons = 24 miles per gallon

Step 3: Find Total Distance for 3.75 Gallons

The car travels  24 miles per gallon . 
 It used  3.75 gallons . 
 So total distance =  24 × 3.75 = 90 miles .  
The correct answer is  90 miles (E).

This question is discussed  here.

A Different Kind of Fuel Problem

This one requires a little algebra:

A car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city. If the car traveled 6 fewer miles per gallon in the city than on the highway, how many miles per gallon did the car travel in the city?
 
 (A) 14
 (B) 16
 (C) 21
 (D) 22
 (E) 27

Step 1: Identify What’s Given

Miles per tank on highway  = 462 
  Miles per tank in city  = 336 
  City miles per gallon  = Highway miles per gallon - 6

Step 2: Set Up an Equation

We define  G  as the number of gallons in a full tank.

Highway miles per gallon =  462 / G  
 City miles per gallon =  336 / G  
 We are told:  (462/G) - (336/G) = 6

Step 3: Solve for G

(462 - 336)/G = 126/G  
  126/G = 6  
  G = 21

Step 4: Find City Miles per Gallon

City MPG = 336 / 21 = 16

So the correct answer is  16 (B).

This question is discussed  here .

A More Challenging Example

An experimental vehicle averages x miles per gallon when driven in the city and 2x miles per gallon when driven on the highway. If the vehicle averages 28 miles per gallon when driven 120 miles in the city and 300 miles on the highway, what is the value of x?
 
 A. 14
 B. 16
 C. 18
 D. 20
 E. 28

Step 1: Identify Given Information

City fuel efficiency  = x miles per gallon 
  Highway fuel efficiency  = 2x miles per gallon 
  Total miles driven  = 120 (city) + 300 (highway) = 420 miles 
  Average fuel consumption  = 28 miles per gallon

Step 2: Set Up the Equation

Total gallons used =  (120 miles / x) + (300 miles / 2x)

Since average fuel efficiency is total miles / total gallons, we set up:

420 /   = 28

420 / (270/x) = 28

14x / 9 = 28

x = 18

So the correct answer is  18 (C).

This question is discussed  here .

Key Takeaways

Look for the common unit  (distance or time) and use it to switch between rates. 
  Set up clear relationships  between speed and fuel consumption. 
  Use algebra for trickier cases  where direct conversion isn’t obvious.  
Once you get used to these patterns, GMAT fuel rate problems will become much more manageable!

Krunaal · Answer

samriddhi1234 · Answer

exactly what I was looking for - this is SUPER helpful. thanks  Krunaal !

Miles, Gallons, and Math: Mastering Fuel Efficiency Questions

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