document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1089549>Question 1089549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two recording devices are set 2600 feet apart, with the device at point A to the west of the device at point B. At a point on a line between the devices, 300 feet from point B, a small amount of explosive is detonated. The recording devices record the time the sound reaches each one. How far directly north of site B should a second explosion be done so that the measured time difference recorded by the devices is the same as that for the first detonation? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #703906 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=703906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not sure if this is correct, but this is what i got.\r<BR>\n" );
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document.write( "it appears to be reasonable.\r<BR>\n" );
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document.write( "the distance between point A and B is 2600 feet.\r<BR>\n" );
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document.write( "the original sound is at a point 300 feet from point B.\r<BR>\n" );
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document.write( "this means it is 2300 feet from point A.\r<BR>\n" );
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document.write( "the difference in feet from the point of the sound to point A and the from the point of the sound to point B is 2000 feet.\r<BR>\n" );
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document.write( "since the sound always travels at the same speed, then if the difference in feet is the same, then the difference in the measured time should be the same.\r<BR>\n" );
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document.write( "so you draw a triangle ABC\r<BR>\n" );
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document.write( "AB is equal to 2600\r<BR>\n" );
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document.write( "BC is equal to x\r<BR>\n" );
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document.write( "AC is equal to x + 2000.\r<BR>\n" );
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document.write( "you use the pythagorean formula to find the value of x and x + 2000.\r<BR>\n" );
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document.write( "x is equal to 690 and x + 2000 is equal to 2690.\r<BR>\n" );
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document.write( "the formula is 2600^2 + x^2 = (x + 2000)^2\r<BR>\n" );
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document.write( "the formula becomes 2600^2 + x^2 = x^2 + 4000x + 2000^2\r<BR>\n" );
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document.write( "the x^2 cancels out.\r<BR>\n" );
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document.write( "you then solve for x to get x = (2600^2 - 2000^2) / 4000 which is equal to 690.\r<BR>\n" );
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document.write( "x + 2000 then becomes 2690.\r<BR>\n" );
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document.write( "the speed of sound is irrelevant to this problem since it is the same for all distances.\r<BR>\n" );
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document.write( "assume the speed of sound is S.\r<BR>\n" );
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document.write( "since the source of the original sound is 300 feet from point B and 2300 feet from point A, then the difference in the time the sound reaches point B and point A would be 2300/S - 300/S which is equal to (2300 - 300) / S which is equal to 2000 / S.\r<BR>\n" );
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document.write( "if the new sound is at point C, then the time it takes for the sound to get to point A is 2690 / S and the time it takes for the sound to get to point A is 690 / S\r<BR>\n" );
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document.write( "the difference in the time is 2690 / S - 690 / S which is equal to (2690 - 690) / S which is equal to 2000 / S.\r<BR>\n" );
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document.write( "the difference is the same.\r<BR>\n" );
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document.write( "my diagram is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/080302.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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