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By the end of this section, you will be able to:
  • Use the distance, rate, and time formula
  • Solve a formula for a specific variable

Before you get started, take this readiness quiz.

  1. Write 35 miles per gallon as a unit rate.
    If you missed this problem, review Ratios and Rates .
  2. Solve 6 x + 24 = 96 .
    If you missed this problem, review Solve Equations with Variables and Constants on Both Sides .
  3. Find the simple interest earned after 5 years on $1,000 at an interest rate of 4% .
    If you missed this problem, review Solve Simple Interest Applications .

Use the distance, rate, and time formula

One formula you’ll use often in algebra and in everyday life is the formula for distance traveled by an object moving at a constant speed. The basic idea is probably already familiar to you. Do you know what distance you travel if you drove at a steady rate of 60 miles per hour for 2 hours? (This might happen if you use your car’s cruise control while driving on the Interstate.) If you said 120 miles, you already know how to use this formula!

The math to calculate the distance might look like this:

distance = ( 60 miles 1 hour ) ( 2 hours ) distance = 120 miles

In general, the formula relating distance, rate, and time is

distance = rate · time

Distance, rate and time

For an object moving in at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula

d = r t

where d = distance, r = rate, and t = time.

Notice that the units we used above for the rate were miles per hour, which we can write as a ratio m i l e s h o u r . Then when we multiplied by the time, in hours, the common units ‘hour’ divided out. The answer was in miles.

Jamal rides his bike at a uniform rate of 12 miles per hour for 3 1 2 hours. How much distance has he traveled?

Solution

Step 1. Read the problem.
You may want to create a mini-chart to summarize the
information in the problem.
d = ?
r = 12 mph
t = 3 1 2 hours
Step 2. Identify what you are looking for. distance traveled
Step 3. Name. Choose a variable to represent it. let d = distance
Step 4. Translate.
Write the appropriate formula for the situation.
Substitute in the given information.
d = r t

d = 12 3 1 2
Step 5. Solve the equation. d = 42 miles
Step 6. Check: Does 42 miles make sense?
.
Step 7. Answer the question with a complete sentence. Jamal rode 42 miles.
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Lindsay drove for 5 1 2 hours at 60 miles per hour. How much distance did she travel?

330 mi

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Trinh walked for 2 1 3 hours at 3 miles per hour. How far did she walk?

7 mi

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Rey is planning to drive from his house in San Diego to visit his grandmother in Sacramento, a distance of 520 miles. If he can drive at a steady rate of 65 miles per hour, how many hours will the trip take?

Solution

Step 1. Read the problem.
Summarize the information in the problem.
d = 520 miles
r = 65 mph
t = ?
Step 2. Identify what you are looking for. how many hours (time)
Step 3. Name:
Choose a variable to represent it.
let t = time
Step 4. Translate.
Write the appropriate formula.
Substitute in the given information.
d = r t
520 = 65 t
Step 5. Solve the equation. t = 8
Step 6. Check:
Substitute the numbers into the formula and make sure
the result is a true statement.
d = r t
520 = ? 65 8
520 = 520>
Step 7. Answer the question with a complete sentence.
We know the units of time will be hours because
we divided miles by miles per hour.
Ray's trip will take 8 hours.
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Questions & Answers

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Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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