Answer:
32 Miles
Step-by-step explanation:
Okay so this will take a moment:
Let's set up the following variables:
d = total distance of the trip
v = 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:
d - 35v = 65
d - 63v = 44
d - 79v = x
The equations being read as:
[total distance] - [time and rate of travel] = [distance remaining]
Now if we restructure each of those equations, you will have:
d = 35v + 65
d = 63v + 44
d = 79v + x
Now you can treat this like a system of equations. First we will solve for the variable: v
Since the total distance remains the same, we can set up the following equation:
subtract 35v from both sides
subtract 44 from both sides
Now if we turn it around:
The common factor of both of these numbers is 7, so divide both by 7:
Therefore:
- v = [tex]\frac{3}{4}[/tex]
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( [tex]\frac{3}{4}[/tex] ) + 65
Solve, and you get:
d = 91.25 miles = [tex]\frac{365}{4}[/tex] miles
Now that you know what the variables: v and d , you can solve for x in the other equation: d = 79v + x
[tex]\frac{365}{4}[/tex] = 79 ( [tex]\frac{3}{4}[/tex] ) + x
Multiply.
[tex]\frac{365}{4}[/tex] = [tex]\frac{237}{4}[/tex] + x
Subtract.
[tex]\frac{365}{4}[/tex] - [tex]\frac{237}{4}[/tex] = x
Simplify.
x = [tex]\frac{128}{4}[/tex] = 32
Voila! 32 Miles to go! Good Luck!
