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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?


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?


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

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
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what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
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Ramkumar Reply
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preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
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