Math Problem Statement
Titus took 30
minutes to walk 2
miles at a constant rate.
d
is the distance Titus walks, in miles.
t
is the time it takes Titus to walk, in minutes.
Write two different equations to represent the relationship between d
and t
.
Solution
To represent the relationship between the distance d
and time t
, we can use two different approaches based on the information given. Since Titus walks at a constant rate, we can use the concept of rate (speed) to form these equations.
1. Using the formula for constant speed:
The general formula for speed (rate) is:
Given that Titus walks 2 miles in 30 minutes, his speed is:
So, the first equation representing the relationship between distance and time is:
2. Rearranging the speed equation:
We can also rearrange the same relationship in a different form to express time in terms of distance . From the speed equation:
Thus, the second equation is:
Summary of the two equations:
These two equations show the relationship between distance and time for Titus walking at a constant rate.
Would you like more details on any of the steps? Here are some follow-up questions:
- How can we find the time taken to walk any distance using the second equation?
- What is the distance walked if Titus walks for 45 minutes?
- How would we graph the relationship between distance and time?
- What does the slope of the graph of represent?
- If Titus walks for 1 hour, how far does he walk?
Tip: In word problems, identifying the rate is key to setting up equations for distance, time, and speed.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Rates
Formulas
Speed = Distance / Time
d = (1/15)t
t = 15d
Theorems
Concept of Constant Speed
Suitable Grade Level
Grades 6-8
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