Precalculus problem, please help

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atenea

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You and a friend live 4 miles apart (on the same "east-west" street) and are talking on the phone. You hear thunder produced by lightning in a storm, and 18 seconds later your friend hears the thunder. Find an equation that gives the possible places where the lightning could have occurred. (He assumes that the coordinate system is measured in feet and that sound travels at 1100 feet per second.)
 

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Set up a coordinate system with the origin is half way between "you" and "your friend". You and your friend live 4 miles apart which is 4(5280)= 21120 feet so "you" are at (10560, 0) and "your friend" is at (-10560, 0). Take (x, y)to be the point where the lightening occurs. The distance from you to the lightening is sqrt(x- 10560)^2+ y^2) so how long does it take for you to hear it? (The distance divided by the speed of sound. That will, of course, be a function of x and y.) The distance from your friend to the lightening is sqrt(x+ 10560)^2+ y^2). How long does it take you friend to hear it? Set the first time equal to the second time plus 18 seconds.
 
HallsofIvy said:
Set up a coordinate system with the origin is half way between "you" and "your friend". You and your friend live 4 miles apart which is 4(5280)= 21120 feet so "you" are at (10560, 0) and "your friend" is at (-10560, 0). Take (x, y)to be the point where the lightening occurs. The distance from you to the lightening is sqrt(x- 10560)^2+ y^2) so how long does it take for you to hear it? (The distance divided by the speed of sound. That will, of course, be a function of x and y.) The distance from your friend to the lightening is sqrt(x+ 10560)^2+ y^2). How long does it take you friend to hear it? Set the first time equal to the second time plus 18 seconds.
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thank you sm for answering!
 
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