Distance, Rate, and Time
For an object moving 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
example
Jamal rides his bike at a uniform rate of
12 miles per hour for
321 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=12mph
t=321hours |
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⋅321 |
Step 5. Solve the equation. |
d=42 miles |
Step 6. Check: Does 42 miles make sense?
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|
Step 7. Answer the question with a complete sentence. |
Jamal rode 42 miles. |
In the following video we provide another example of how to solve for distance given rate and time.
https://youtu.be/lMO1L_CvH4Y
Example
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?
Answer:
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=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=?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. |
Rey's trip will take 8 hours. |
In the following video we show another example of how to find rate given distance and time.
https://youtu.be/3rYh32ErDaE