Math Problem Statement
The table below shows a jogger's time t, in minutes, and distance traveled d, in miles.
t d 12 0.90 16 1.20 22 1.65
Which equation represents the relationship between t and d? A.d = 0.075t B.t = 0.075d C.d = t – 11.1 D.t + 4 = d + 0.3
Solution
To determine the equation that represents the relationship between time (in minutes) and distance (in miles), we can begin by observing the table of values provided:
(minutes) | (miles) |
---|---|
12 | 0.90 |
16 | 1.20 |
22 | 1.65 |
Step 1: Check if the relationship is linear.
From the data, it looks like there may be a linear relationship between and . Let's test this by checking the differences between consecutive values of and .
- Difference in : ,
- Difference in : ,
The differences in and aren't exactly proportional, but this suggests the relationship could be linear with a slope.
Step 2: Check the slope of the linear relationship.
We can calculate the slope of the line using two points and :
Using the points and :
This gives a slope of 0.075, which suggests that the distance increases by 0.075 miles for every 1 minute increase in time .
Step 3: Form the equation.
Since the relationship between and is linear with a slope of 0.075, the equation for as a function of is:
Step 4: Compare with the given options.
The correct equation is:
A.
This matches the form of the equation we derived.
Would you like more details or explanations?
Here are 5 related questions for further exploration:
- How would the equation change if the jogger increased their speed?
- What is the jogger's speed in miles per minute based on the equation?
- Can you calculate the distance the jogger would travel in 30 minutes using this equation?
- How would the graph of this linear relationship look?
- How does this equation apply to other forms of travel (e.g., biking or driving)?
Tip: To verify if an equation is correct, always check it with multiple points from the data set.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope
Formulas
Slope formula: m = (d2 - d1) / (t2 - t1)
Linear equation: d = mt
Theorems
Linear relationship between two variables
Suitable Grade Level
Grades 7-9
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