SOLUTION: Two cars leave an intersection. One car travels north; the other travels east. When the car traveling north had gone 24 miles, the distance between the cars was four miles more th

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Two cars leave an intersection. One car travels north; the other travels east. When the car traveling north had gone 24 miles, the distance between the cars was four miles more th      Log On


   



Question 210931: Two cars leave an intersection. One car travels north; the other travels east. When the car traveling north had gone 24 miles, the distance between the cars was four miles more than three times the distance traveled by the car heading east. Find the distance between the cars at that time
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let e= distance travelled by the
car going east when the car going north
has gone 24 mi
given:
Distance between the cars is
3e+%2B+4
Using the pythagorean theorem, I can say
24%5E2+%2B+e%5E2+=+%283e+%2B+4%29%5E2
576+%2B+e%5E2+=+9e%5E2+%2B+24e+%2B+16
8e%5E2+%2B+24e+-+560+=+0
e%5E2+%2B+3e+-+70+=+0
Using the quadratic formula:
e+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+3
c+=+-70
e+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-70%29+%29%29%2F%282%2A1%29+
e+=+%28-3+%2B-+sqrt%28+9+%2B+280+%29%29%2F2+
e+=+%28-3+%2B-+sqrt%28+289+%29%29%2F2+
e+=+%28-3+%2B-+17%29%2F2+
e+=+%28-3+-+17%29%2F2 (Can't use this answer)
e+=+%28-3+%2B+17%29%2F2
e+=+14%2F2
e+=+7
and, since distance between the cars is
3e+%2B+4
3%2A7+%2B+4+=+25 mi
The distance between the cars is 25 mi
check:
24%5E2+%2B+7%5E2+=+25%5E2
576+%2B+49+=+625
625+=+625
OK