<< Chapter < Page Chapter >> Page >
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?


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.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Lindsay drove for 5 1 2 hours at 60 miles per hour. How much distance did she travel?

330 mi

Got questions? Get instant answers now!

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

7 mi

Got questions? Get instant answers now!

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?


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.
Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where is the latest information on a no technology how can I find it
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Berger describes sociologists as concerned with
Mueller Reply
what is hormones?
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
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.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now

Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Prealgebra' conversation and receive update notifications?