document.write( "Question 165303: distance between point A & point B = 310 KM . two person leave these points at the same time , one with speed of 106km/h and the other with 87km/h . How long does it take to meet each other ? \n" ); document.write( "

Algebra.Com's Answer #121862 by gonzo(654) $\"\"$ $\"About$

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AB = 310 km.
\n" ); document.write( "AC = x
\n" ); document.write( "BC = 310-x
\n" ); document.write( "-----
\n" ); document.write( "T = time
\n" ); document.write( "-----
\n" ); document.write( "person leaving from point A is traveling at 87km/h.
\n" ); document.write( "person leaving from point B is traveling at 106km/h.
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\n" ); document.write( "they both meet at point C.
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\n" ); document.write( "person leaving from point A travels x kilometers in T hours.
\n" ); document.write( "person leaving from point B travels (310-x) kilometers in T hours.
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\n" ); document.write( "rate * time = distance
\n" ); document.write( "-----
\n" ); document.write( "person leaving from A equation:
\n" ); document.write( "87*T = x
\n" ); document.write( "-----
\n" ); document.write( "person leaving from B equation:
\n" ); document.write( "106*T = 315-x
\n" ); document.write( "-----
\n" ); document.write( "solve both equations for T
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\n" ); document.write( "T = x/87 (first equation)
\n" ); document.write( "T = (315-x)/106 (second equation)
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\n" ); document.write( "since they both equal T then they both equal each other.
\n" ); document.write( "x/87 = (315-x)/106
\n" ); document.write( "-----
\n" ); document.write( "multiply both sides by (87*106)
\n" ); document.write( "equation becomes
\n" ); document.write( "106*x = (315-x)*87
\n" ); document.write( "remove parentheses.
\n" ); document.write( "106*x = 315*87 - 87*x
\n" ); document.write( "add 87*x to both sides.
\n" ); document.write( "106*x + 87*x = 315*87
\n" ); document.write( "perform operations shown.
\n" ); document.write( "193*x = 27405
\n" ); document.write( "divide both sides by 193.
\n" ); document.write( "x = 141.9948187
\n" ); document.write( "solve for T in first equation.
\n" ); document.write( "x/87 = T
\n" ); document.write( "141.9948187/87 = T
\n" ); document.write( "T = 1.632124352
\n" ); document.write( "-----
\n" ); document.write( "315-x = 173.0051813
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\n" ); document.write( "calculate T from second equation.
\n" ); document.write( "T = (315-x)/106
\n" ); document.write( "T = 173.0051813/106
\n" ); document.write( "T = 1.632124352
\n" ); document.write( "-----
\n" ); document.write( "point C is 141.9948187 miles from A
\n" ); document.write( "point C is 173.0051813 miles from B
\n" ); document.write( "AC + BC = 315.
\n" ); document.write( "-----
\n" ); document.write( "rate of travel equals distance over time.
\n" ); document.write( "141.9948187 / 1.632124352 = 87 km/h
\n" ); document.write( "173.0051813 / 1.632124352 = 106 km/h
\n" ); document.write( "-----
\n" ); document.write( "answer is T = 1.632124352 hours
\n" ); document.write( "They will meet at point C in 1.632124352 hours\r
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