From the equation, it looks like we can set up a triangle like this. One side is x and the other is x + 20 because the northbound car traveled 20 miles farther. The hypotenuse is 100 because they were 100 miles apart.
Next, we can use the Pythagorean Theorem to solve for x:
a² + b² = c²
x² + (x + 20)² = 100²
This simplifies to:
x² + x² + 40x + 400 = 10000
2x² + 40x = 9600
2x² + 40x - 9600 = 0
After that, we can divided each side by 2:
x² + 20x - 4800 = 0
Next, we have to factor:
(x - 60)(x + 80) = 0
x = 60, -80
Since we know that distance can't be negative, 60 is the valid answer in this case.
x = 60
x + 20 = 80
Using this information, we know that the westbound car traveled 60 miles and the northbound car traveled 80 miles.
