SOLUTION: Two cars leave an intersection. One car travels North the other travels East. When the car traveling North had gone 63 miles, the distance between the cars was 17 miles more than t

Question 698932: Two cars leave an intersection. One car travels North the other travels East. When the car traveling North had gone 63 miles, the distance between the cars was 17 miles more than three times the distance traveled by the car heading East. Find the distance between the cars at that time.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two cars leave an intersection. One car travels North the other travels East.
When the car traveling North had gone 63 miles, the distance between the cars was 17 miles more than three times the distance traveled by the car heading East.
Find the distance between the cars at that time.
:
This is a Pythagoras problem a^2 + b^2 = c^2, where:
a = 63, northbound car dist)
b = Eastbound car dist
c = distance between the cars at this time
"the distance between the cars was 17 miles more than three times the distance traveled by the car heading East
c = 3b + 17
:
63^2 + b^2 = (3b+17)^2
FOIL the right side
3969 + b^2 = 9b^2 + 51b + 51b + 289
Combine like terms on the right
0 = 9b^2 - b^2 + 102b + 289 - 3969
0 = 8b^2 + 102b - 3680
Simplify, divide by 2
4b^2 + 51b - 1840 = 0
Use the quadratic formula to find b
the positive solution should be b = 16
then
3(16) + 17 = 65 mi is the distance between the cars at this time
;
:
Check this on your calc: enter results: 65
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