SOLUTION: Two cars leave an intersection. One car travels east; the other north. when the car traveling east had gone 15 miles, the distance between the cars was 5 miles more than the distan

Question 268067: Two cars leave an intersection. One car travels east; the other north. when the car traveling east had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading north. How far had the northbound car traveled?
Thank you for your help. I am stumped on how to set up this problem for solving.
Thank you, Nora
Found 2 solutions by Alan3354, ptaylor:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Two cars leave an intersection. One car travels east; the other north. when the car traveling east had gone 15 miles, the distance between the cars was 5 miles more than the distance traveled by the car heading north. How far had the northbound car traveled?
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The distance between the cars is the hypotenuse of the right triangle formed by the 2 distances from the intersection.
E = 15 (eastbound car)
d^2 = E^2 + N^2
d = N + 5
(N+5)^2 = 15^2 + N^2
N^2 + 10N + 25 = 225 + N^2
10N = 200
N = 20 miles

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Hi Nora---
Lets see what we can do:
Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r
Let d=distance that the northbound car travelled
Now know that we have a right triangle to deal with here and the distance between the two cars is the hypotenuse of the right triangle.
The base of the right triangle (car travelling east) is 15 mi; the hypotneuse is (d+5) and the other side is d(car travelling north).
Applying the pythagorean theorem, we have:
(d+5)^2=15^2+d^2 expand the left side and simplify
d^2+10d+25=225+d^2 subtract d^2 and also 25 from each side
d^2-d^2+10d+25-25=225-25+d^2-d^2 collect like terms
10d=200 divide each side by 10
d=20 mi-------------------distance travelled by northbound car
distance between the cars=d+5=20+5=25 mi
CK
25^2=15^2+20^2
625=225+400
625=625
Does this help?---ptaylor

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