document.write( "Question 438718: tessa can ride her bike 24 miles in 1 hour less time than it takes Gary to walk 9 miles. tessa's rate is 9 miles per hour faster than Gary's rate. find tessa's rate. \n" ); document.write( "
Algebra.Com's Answer #303312 by sudheerb(5)\"\" \"About 
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Let the rates of Tessa and Gary be T and G.
\n" ); document.write( "Given that Tessa's rate is 9 miles per hour faster than Gary's rate.
\n" ); document.write( "So, Gary's rate is 9 miles per hour less than Tessa's rate.
\n" ); document.write( "Therefore G = T - 9 ...(1)
\n" ); document.write( "We know that rate = distance/time
\n" ); document.write( "Time taken by Tessa to cover 24 miles by bike is t1 = distance/ rate
\n" ); document.write( " t1 = 24/T
\n" ); document.write( "Time taken by Gary to cover 9 miles by walk is t2 = distance/rate
\n" ); document.write( " t2 = 9/G
\n" ); document.write( "Given that tessa can ride her bike 24 miles in 1 hour less time than it takes Gary to walk 9 miles.
\n" ); document.write( " So, t2 - t1 = 1
\n" ); document.write( " 9/G - 24/T = 1
\n" ); document.write( "(9T - 24G)/GT = 1
\n" ); document.write( "9T - 24G = GT\r
\n" ); document.write( "\n" ); document.write( "From equation (1), we have G = T - 9.
\n" ); document.write( "9T - 24(T-9) = (T-9)T
\n" ); document.write( "9T - 24T + 216 = T^2 - 9T
\n" ); document.write( "-15T + 216 = T^2 - 9T [Add 15T to both sides of equation]
\n" ); document.write( "-15T + 216 + 15T = T^2 - 9T + 15T
\n" ); document.write( "216 = T^2 - 9T + 15T\r
\n" ); document.write( "\n" ); document.write( "216 = T^2 + 6T [subtract 216 from both sides of equation]
\n" ); document.write( "216 - 216 = T^2 + 6T - 216
\n" ); document.write( "0 = T^2 + 6T - 216
\n" ); document.write( "T^2 + 6T - 216 = 0\r
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"aT%5E2%2BbT%2Bc=0\" (in our case \"1T%5E2%2B6T%2B-216+=+0\") has the following solutons:
\n" ); document.write( "
\n" ); document.write( " \"T%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
\n" ); document.write( "
\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%286%29%5E2-4%2A1%2A-216=900\".
\n" ); document.write( "
\n" ); document.write( " Discriminant d=900 is greater than zero. That means that there are two solutions: \"+x%5B12%5D+=+%28-6%2B-sqrt%28+900+%29%29%2F2%5Ca\".
\n" ); document.write( "
\n" ); document.write( " \"T%5B1%5D+=+%28-%286%29%2Bsqrt%28+900+%29%29%2F2%5C1+=+12\"
\n" ); document.write( " \"T%5B2%5D+=+%28-%286%29-sqrt%28+900+%29%29%2F2%5C1+=+-18\"
\n" ); document.write( "
\n" ); document.write( " Quadratic expression \"1T%5E2%2B6T%2B-216\" can be factored:
\n" ); document.write( " \"1T%5E2%2B6T%2B-216+=+1%28T-12%29%2A%28T--18%29\"
\n" ); document.write( " Again, the answer is: 12, -18.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-216+%29\"

\n" ); document.write( "\n" ); document.write( "Here T cannot be equal to -18.
\n" ); document.write( "Hence T = 12.
\n" ); document.write( "Therefore rate of Tessa's is 12 miles per hour.\r
\n" ); document.write( "\n" ); document.write( "Regards,
\n" ); document.write( "Sudheer(edurite.com)
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