Sabrina G. answered • 12/19/17
Tutor
New to Wyzant
Confusion to Clarity
This basically makes a triangle.
Draw a dot on piece of paper. This point represents the intersection.
The motorcycle travels south. Draw a line down from the dot that represents the motorcycle driving for 20 minutes. We will label this as "x" miles since most of the word problem is in relationship to the distance the motorcycle traveled.
The car travels east. Draw a new line from the intersection dot to the right. This line represents the car driving east for 20 minutes. Since the car is 7 miles farther than the motorcycle from the intersection we'll label this line "x + 7" miles
The last line you'll draw from the unconnected ends of the lines. This is the distance the two vehicles are from each other after the 20 minutes, which is 8 miles more than the motorcycles distance from the intersection. This line becomes "x+8"
Since one vehicle went south and the other went east, they drove away from each other at a 90 degree angle. This is a right triangle. Thus, the sum of the squares of the two shorter sides equals the square of the longest side (a2+b2=c2). So:
x2 + (x+7)2= (x+8)2
x2 + (x+7)(x+7)= (x+8)(x+8)
x2 + x2+14x+49= x2+16x+64 The two x2 s on the left can be added together.
2x2+14x+49=x2+16x+64 Now solve for 0 (getting everything onto the left side and 0 on the right side)
-64 -64
2x2+14x-15=x2+16x
-16x -16x
2x2- 2x-15= x2
-x2 -x2
x2-2x-15 = 0 Factor
(x+3)(x-5)=0
x+3=0 x= -3
x-5=0 x= 5
x= -3 & 5
But the practical domain of the word problem means that x must be more than 0 (aka a positive number) so x=5.
Apply this to the triangle.
The distance between the motorcycle and the intersection is x=5 miles
The distance between the car and the intersection is x+7= 5+7= 12 miles
The distance between the car and the motorcycle is x+8 = 5+8=13 miles
The answer is 13 miles.
You can double check this:
a2+b2=c2
52+122=132
25+144=169
169=169
