Math Word Problems for Firefighter Exam Study Guide

Distance Formula: Distance = Rate × Time

The key words are movement words such as: plane, train, boat, car, walk, run, climb, swim, travel. It is also helpful to carry units on distance problems.

• How far did the plane travel in 4 hours if it averaged 300 miles per hour?

D =

D = 1,200 miles

• Ben walked 20 miles in 4 hours. What was his average speed       20 miles = r × 4 hours



5 miles per hour = r

Solving a Word Problem Using the Translation Table

Remember the problem at the beginning of this chapter about the jellybeans?

Juan ate of the jellybeans. Maria then ate of the remaining jellybeans, which left 10 jellybeans. How many jellybeans were there to begin with?

1. 60
2. 90
3. 120
4. 140

We solved it by working backward. Now let's solve it using our translation rules.

Assume Juan started with J jellybeans. Eating of them means eating × J jellybeans. Maria ate a fraction of the remaining jellybeans, which means we must subtract to find out how many are left: J – × J = × J. Maria then ate , leaving of the × J jellybeans, or × × J jellybeans. Multiplying out × × J gives J as the number of jellybeans left. The problem states that there were 10 jellybeans left, meaning that we set × J equal to 10: × J = 10 Solving this equation for J gives J = 60. Thus, the right answer is a (the same answer we got when we worked backward). As you can see, both methods—working backwards and translating from text to math—work. You should use whichever method is more comfortable for you.

Practice Word Problems

You will find word problems using fractions, decimals, and percentages in those sections of this chapter. For now, practice using the translation table on problems that just require you to work with basic arithmetic.

1. Joan went shopping with $100 and returned home with only $18.42.How much money did she spend?
   1. $81.58
   2. $72.68
   3. $72.58
   4. $71.68
2. Mary invited 10 friends to a party. Each friend brought 3 guests. How many people came to the party, excluding Mary?
   1. 3
   2. 10
   3. 30
   4. 40
3. The office secretary can type 80 words per minute on his word processor. How many minutes will it take him to type a report containing 760 words?
   1. 8
   2. 
   3. 
   4. 10
4. Mr. Wallace is writing a budget request to upgrade his personal computer system. He wants to purchase 4 mb of RAM, which will cost $100, two new software programs at $350 each, a tape backup system for $249, and an additional tape for $25.What is the total amount Mr.Wallace should write on his budget request?
   1. $724
   2. $974
   3. $1,049
   4. $1,074

Answers

1. a.
2. d.
3. c.
4. d.