document.write( "Question 1144577: A motorist travels a distance of 84km. He finds that; if on the return journey he increases his average speed by 4km/h, he will take half an hour less.
\n" ); document.write( "What was his average speed for the first part of the journey?
\n" ); document.write( "How long did he take for the double journey?
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Algebra.Com's Answer #765732 by Theo(13342)\"\" \"About 
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basic formuls ia r * t = d
\n" ); document.write( "r is the rate
\n" ); document.write( "t is the time
\n" ); document.write( "d is the distance\r
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\n" ); document.write( "\n" ); document.write( "if d = 84 kilometers, then the formula becomes r * t = 84
\n" ); document.write( "that would be the formula going.
\n" ); document.write( "on the return, the speed is increased by 4 kilometers per hour and the time is half an hour less.
\n" ); document.write( "the formula for the return journey becomes:
\n" ); document.write( "(r + 4) * (t - .5) = 84\r
\n" ); document.write( "\n" ); document.write( "you have 2 equations that need to be solved simultaneously.
\n" ); document.write( "they are:
\n" ); document.write( "r * t = 84
\n" ); document.write( "(r + 4) * (t - .5) = 84
\n" ); document.write( "in the first equation, solve for r to get:
\n" ); document.write( "r = 84/t
\n" ); document.write( "in the second equation, replace r with that to get:
\n" ); document.write( "(84/t + 4) * (t - .5) = 84
\n" ); document.write( "multiply both sides of that equation by t to get:
\n" ); document.write( "(84 + 4 * t) * (t - .5) = 84 * t
\n" ); document.write( "simplify by completing the indicated multiplication to get:
\n" ); document.write( "84 * (t - .5) + 4 * t * (t - .5) = 84 * t
\n" ); document.write( "simplify further to get:
\n" ); document.write( "84 * t - 42 + 4 * t^2 - 2 * t = 84 * t
\n" ); document.write( "subtract 84 * t from both sides of the equation to get:
\n" ); document.write( "84 * t - 84 * t - 42 + 4 * t^2 - 2 * t = 0
\n" ); document.write( "combine like terms and order in descending order of degree to get:
\n" ); document.write( "4 * t^2 - 2 * t - 42 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "t = 3.5 or t = -3
\n" ); document.write( "t has to be positive so t = 3.5.\r
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\n" ); document.write( "\n" ); document.write( "in the first equation, solve for r to get r = 84 / 3.5 = 24.
\n" ); document.write( "first equation of r*t = 84 becomes 3.5 * 24 = 84 which becomes 84 = 84 which is true.\r
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\n" ); document.write( "\n" ); document.write( "in the second equation, replace r with 24 and t with 3.5 to get:
\n" ); document.write( "(r + 4) * (t - .5) = 84 becomes 28 * 3 = 84 which becomes 84 = 84 which is true.\r
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\n" ); document.write( "\n" ); document.write( "r = 24 and t = 3.5 is confirmed to be good.
\n" ); document.write( "the average speed for the first part of the journey is 24 kilometers per hour.
\n" ); document.write( "the journey there took 3.5 hours and the journey back took 3 hours for a total of 6.5 hours.\r
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