document.write( "Question 781457: The Word Problem:
\n" ); document.write( " Tina is training for a biathlon. To train for the running portion of the race, she runs 8 miles each day over the same course. The first 2 miles of the course is on level ground, while the last 6 miles is downhill. She runs 3 miles per hour slower on level ground than she runs downhill. If the complete course takes 1 hour, how fast does she run on the downhill part of the course?\r
\n" ); document.write( "\n" ); document.write( "My Trouble:
\n" ); document.write( " I've tried this problem and came to the solution 5.5 MPH downhill using the equation: $\"+%28+x-3+%29+%2B+x+=+8\"$ . However I have been told this is not the correct answer. I know my math is solid on my equation, thus I must have the wrong equation. My thinking behind using this equation was that because her speed downhill is unknown it must be represented by a variable, and her speed on flat ground is 3 less then her speed downhill and so by adding the two we have her total speed over the whole course. I feel as though I'm missing something but I can't figure out exactly what. \n" ); document.write( "

Algebra.Com's Answer #475974 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
To train for the running portion of the race, she runs 8 miles each day over the same course.
\n" ); document.write( " The first 2 miles of the course is on level ground, while the last 6 miles is downhill.
\n" ); document.write( " She runs 3 miles per hour slower on level ground than she runs downhill.
\n" ); document.write( " If the complete course takes 1 hour, how fast does she run on the downhill part of the course?
\n" ); document.write( "Let s = speed downhill
\n" ); document.write( "then
\n" ); document.write( "(s-3) = speed on level ground
\n" ); document.write( ":
\n" ); document.write( "Write a time equation.time = dist/speed
\n" ); document.write( "level time + downhill time = 1 hr
\n" ); document.write( " $\"2%2F%28%28s-3%29%29\"$ + $\"6%2Fs\"$ = 1
\n" ); document.write( "multiply by s(s-3), resulting in
\n" ); document.write( "2s + 6(s-3) = s(s-3)
\n" ); document.write( "2s + 6s - 18 = s^2 - 3s
\n" ); document.write( "Arrange as a quadratic equation on the right
\n" ); document.write( "0 = s^2 - 3s - 8s + 18
\n" ); document.write( "s^2 - 11s + 18 = 0
\n" ); document.write( "factors to
\n" ); document.write( "(s-2)(s-9) = 0
\n" ); document.write( "s = 9 mph is the reasonable solution here
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "See if that works find the time of each
\n" ); document.write( "2/6 + 6/9 = 1 \n" ); document.write( "

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