# 9.7 Solve a formula for a specific variable

 Page 1 / 9
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 $6x+24=96.$
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 $\text{1,000}$ at an interest rate of $\text{4%}.$
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:

$\begin{array}{}\\ \text{distance}=\left(\frac{60\phantom{\rule{0.2em}{0ex}}\text{miles}}{1\phantom{\rule{0.2em}{0ex}}\text{hour}}\right)\left(2\phantom{\rule{0.2em}{0ex}}\text{hours}\right)\hfill \\ \text{distance}=120\phantom{\rule{0.2em}{0ex}}\text{miles}\hfill \end{array}$

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

$\text{distance}\phantom{\rule{0.2em}{0ex}}\text{=}\phantom{\rule{0.2em}{0ex}}\text{rate}·\text{time}$

## 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

$d=rt$

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 $\frac{miles}{hour}.$ 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 $3\frac{1}{2}$ 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. $d=?$ $r=12\phantom{\rule{0.2em}{0ex}}\text{mph}$ $t=3\frac{1}{2}\phantom{\rule{0.2em}{0ex}}\text{hours}$ 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. $d=rt$ $d=12\cdot 3\frac{1}{2}$ Step 5. Solve the equation. $d=42\phantom{\rule{0.2em}{0ex}}\text{miles}$ Step 6. Check: Does 42 miles make sense? Step 7. Answer the question with a complete sentence. Jamal rode 42 miles.

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

330 mi

Trinh walked for $2\frac{1}{3}$ hours at $3$ miles per hour. How far did she walk?

7 mi

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. $d=520\phantom{\rule{0.2em}{0ex}}\text{miles}$ $r=65\phantom{\rule{0.2em}{0ex}}\text{mph}$ $t=?$ 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. $d=rt$ $520=65t$ 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. $d=rt$ $520\stackrel{?}{=}65\cdot 8$ $520=520>✓$ 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.

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Berger describes sociologists as concerned with
what is hormones?
Wellington
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.
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.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
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
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?