document.write( "Question 1085553: I have a assignment on making two linear equations from two animals racing a fair race. The two I picked were African wild dog 45mph and coyote 43mph. How would I make that into an equation. I am so lost and confused \n" ); document.write( "
Algebra.Com's Answer #699636 by Theo(13342)![]() ![]() You can put this solution on YOUR website! assume the race is for 1 mile.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "rate * time = distance.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "for the dog, rate = 45 miles per hour.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "for the coyote, rate = 43 miles per hour.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "let T1 equal the time it takes the dog to run a distance of D1.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "let T2 equal the time it takes the coyote to run a distance of D2.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the formulas become:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "45 * T1 = D1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "43 * T2 = D2\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "if you make the distance that they both run the same, then replace D1 and D2 with D.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you will get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "45 * T1 = D\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "43 * T2 = D\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "if you subtract the second equation from the first, you will get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "45 * T1 - 43 * T2 = 0\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "add 43 * T2 to both sides of the equation to get 45 * T1 = 43 * T2\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "divide both sides of the equation by 45 to get T1 = 43 * T2 / 45\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "simplify to get T1 = .9556 * T2 rounded to 4 decimal digits.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "the dog is faster and will run the same distance in less time than the coyote.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "if you make the time the same, then replace T1 and T2 with T and the formulas become:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "45 * T = D1\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "43 * T = D2\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve both formulas for T to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "T = D1 / 45\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "T = D2 / 43\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "subtract the second equation from the first and you get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "0 = D1/45 - D2/43\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "add D2/43 to both sides of the equation to get D2/43 = D1/45\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "solve for D1 to get D1 = D2/43 * 45.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "simplify to get D1 = 1.0465 * D2 rounded to 4 decimal places.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "given they run the same time, the dog will run 1.0465 times the distance that the coyote will run.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "stand to reason, because the dog is faster than the coyote.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |