Question

NEED HELP 50 POINTS TO WHOEVER CAN ANSWER

Answer 1

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:

• 35v + 65 = 63v + 44

subtract 35v from both sides

• 65 = 28v + 44

subtract 44 from both sides

• 21 = 28v

Now if we turn it around:

• 28v = 21

The common factor of both of these numbers is 7, so divide both by 7:

• 4v = 3

Therefore:

• v = $\frac{3}{4}$

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( $\frac{3}{4}$ ) + 65

Solve, and you get:

d = 91.25 miles = $\frac{365}{4}$ miles

Now that you know what the variables: v and d , you can solve for x in the other equation: d = 79v + x

$\frac{365}{4}$ = 79 ( $\frac{3}{4}$ ) + x

Multiply.

$\frac{365}{4}$ = $\frac{237}{4}$ + x

Subtract.

$\frac{365}{4}$ - $\frac{237}{4}$ = x

Simplify.

x = $\frac{128}{4}$ = 32

Voila! 32 Miles to go! Good Luck!