Answer :
Answer:
B. 7 miles
General Formulas and Concepts:
Algebra I
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Terms/Coefficients
Functions
- Function Notation
Systems of Linear Equations
- Solving methods: Substitution/Elimination
Step-by-step explanation:
Step 1: Define
Identify given.
[Ralph's Walking Distance Function]: d = -6t + 10
[Joan's Bicycle Distance Function]: d = 14t
Step 2: Find Meeting Point
To find where Joan and Ralph will meet, we need to find where they intersect. Therefore, we need to find the time which they both meet up at. To do this, we can use the process of substitution to find our value of t:
- [Equation 1] Substitute in d:
[tex]\displaystyle\begin{aligned}d = -6t + 10 & \rightarrow 14t = -6t + 10\end{aligned}[/tex]
From here, we can simply use techniques listed under "Algebra I" to solve for t:
[tex]\displaystyle\begin{aligned}14t & = -6t + 10 \\20t & = 10 \\t & = \boxed{ \frac{1}{2} } \\\end{aligned}[/tex]
∴ both Joan and Ralph will meet up in half an hour, or 0.5 hours.
Step 3: Find Mileage
To find how many miles they will meet up at, we substitute the number of hours elapsed (found in Step 2) and substitute it into any of the equations given:
[tex]\displaystyle\begin{aligned}d & = 14t \\& = 14 \bigg( \frac{1}{2} \bigg) \\& = \boxed{7} \\\end{aligned}[/tex]
∴ Joan will meet Ralph after 7 miles.
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Topic: Algebra I