Question 645250
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
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Cheers,
Stan H.