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Before you get started, take this readiness quiz.
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:
In general, the formula relating distance, rate, and time is
For an object moving in at a uniform (constant) rate, the distance traveled, the elapsed time, and the rate are related by the formula
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?
Step 1.
Read the problem.
You may want to create a minichart 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?
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. $d=rt$ $520\stackrel{?}{=}65\cdot 8$ $520=\mathrm{520>}\u2713$ 

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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