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.
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document.write( "What was his average speed for the first part of the journey?
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document.write( "How long did he take for the double journey? \n" );
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Algebra.Com's Answer #765732 by Theo(13342)![]() ![]() You can put this solution on YOUR website! 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 \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |