example
Jamal rides his bike at a uniform rate of [latex]12[/latex] miles per hour for [latex]3\frac{1}{2}[/latex] 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. |
[latex]d=?[/latex]
[latex-display]r=12\text{mph}[/latex-display]
[latex]t=3\frac{1}{2}\text{hours}[/latex] |
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. |
[latex]d=rt[/latex]
[latex]d=12\cdot 3\frac{1}{2}[/latex] |
Step 5. Solve the equation. |
[latex]d=42\text{ miles}[/latex] |
Step 6. Check: Does 42 miles make sense?
|
|
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 [latex]520[/latex] miles. If he can drive at a steady rate of [latex]65[/latex] miles per hour, how many hours will the trip take?
Answer:
Solution:
Step 1. Read the problem.
Summarize the information in the problem. |
[latex]d=520[/latex] miles
[latex]r=65[/latex] mph
[latex]t=?[/latex] |
Step 2. Identify what you are looking for. |
how many hours (time) |
Step 3. Name:
Choose a variable to represent it. |
let [latex]t[/latex] = time |
Step 4. Translate.
Write the appropriate formula.
Substitute in the given information. |
[latex]d=rt[/latex]
[latex]520=65t[/latex] |
Step 5. Solve the equation. |
[latex]t=8[/latex] |
Step 6. Check:
Substitute the numbers into the formula and make sure
the result is a true statement.
[latex-display]d=rt[/latex-display]
[latex-display]520\stackrel{?}{=}65\cdot 8[/latex-display]
[latex]520=520\quad\checkmark [/latex] |
|
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 [latex]8[/latex] hours. |
In the following video we show another example of how to find rate given distance and time.
https://youtu.be/3rYh32ErDaE