SOLUTION: How do I go about solving this word problem? Two cars leave an intersection. One car travels north;the other travels east. When the car traveling north had gone 24 miles, the dista

Question 645250: How do I go about solving this word problem? 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 stanbon(75887) (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 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.
Draw the picture on a coordinate system letting the intersection be at (0,0).
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The north-bound car goes to (0,24)
The east-bound car goes to (x,0)
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The distance from (x,0) to (0,24) is as follows:
sqrt(24^2 + x^2) = 3x + 4
Solve for "x":
24^2 + x^2 = 9x^2 + 24x + 16
8x^2 +24x - 560 = 0
x^2 + 3x - 70 = 0
Factor:
(x+10)(x-7) = 0
Positive solution:
x = 7
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Distance between cars is sqrt(24^2 + 7^2) = 25 miles
================
Cheers,
Stan H.

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