Answer:
32 Miles
Step-by-step explanation:
Okay so this will take a moment:
Let's set up the following variables:
<em>d</em> = total distance of the trip
<em>v</em> = some rate of velocity/travel
Note: t is not a variable here as it would denote time, but we know the time, so rate of travel as a variable is next best.
With those variables, we can set up 3 equations as follows:
<em>d - 35v = 65</em>
<em>d - 63v = 44</em>
<em>d - 79v = x</em>
The equations being read as:
[<em>total distance</em>] - [<em>time and rate of travel</em>]<em> = </em>[<em>distance remaining</em>]
Now if we restructure each of those equations, you will have:
<em>d = 35v + 65</em>
<em>d = 63v + 44</em>
<em>d = 79v + x</em>
Now you can treat this like a system of equations. First we will solve for the variable: <em>v</em>
Since the total distance remains the same, we can set up the following equation:
- <em>35v + 65 = 63v + 44</em>
subtract <em>35v</em> from both sides
- <em>65 = 28v + 44</em>
subtract 44 from both sides
- <em>21 = 28v</em>
Now if we turn it around:
- <em>28v = 21</em>
The common factor of both of these numbers is 7, so divide both by 7:
- <em>4v = 3</em>
Therefore:
- <em>v =</em>
That was a lot. NOW that you know the value of v, you can find the total distance that Eric needs to travel, so plug it into one of the equations:
d = 35( ) + 65
Solve, and you get:
<em>d = 91.25 miles = </em> <em>miles</em>
Now that you know what the variables: <em>v</em> and <em>d </em>, you can solve for x in the other equation: <em>d = 79v + x</em>
<em /><em> = 79 </em>(
) + <em>x</em>
Multiply.
<em> = </em>
+ <em>x</em>
Subtract.
-
= x
Simplify.
x = = 32
Voila! 32 Miles to go! Good Luck!