Answer:Solving Linear Equations - Distance, Rate and Time
Objective: Solve distance problems by creating and solving a linear
equation.
An application of linear equations can be found in distance problems. When
solving distance problems we will use the relationship rt = d or rate (speed) times
time equals distance. For example, if a person were to travel 30 mph for 4 hours.
To find the total distance we would multiply rate times time or (30)(4) = 120.
This person travel a distance of 120 miles. The problems we will be solving here
will be a few more steps than described above. So to keep the information in the
problem organized we will use a table. An example of the basic structure of the
table is blow:
Rate Time Distance
Person 1
Person 2
Table 1. Structure of Distance Problem
The third column, distance, will always be filled in by multiplying the rate and
time columns together. If we are given a total distance of both persons or trips we
will put this information below the distance column. We will now use this table to
set up and solve the following example
Example Two joggers start from opposite ends of an 8 mile course running towards each
other. One jogger is running at a rate of 4 mph, and the other is running at a
rate of 6 mph. After how long will the joggers meet?
Rate Time Distance
Jogger 1
Jogger 2
The basic table for the joggers, one and two
Rate Time Distance
Jogger 1 4
Jogger 2 6
We are given the rates for each jogger.
These are added to the table
Rate Time Distance
Jogger 1 4 t
Jogger 2 6 t
We only know they both start and end at the
same time. We use the variable tfor both times
Rate Time Distance
Jogger 1 4 t 4t
Jogger 2 6 t 6t
The distance column is filled in by multiplying
rate by time
8 We have total distance, 8 miles, under distance
4t + 6t = 8 The distance column gives equation by adding
10t = 8 Combine like terms, 4t + 6t
10 10 Divide both sides by 10
t =
4
5
Our solution fort, 4
5
hour(48 minutes)
As the example illustrates, once the table is filled in, the equation to solve is very
easy to find. This same process can be seen in the following example
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