document.write( "Question 1055874: Tina is training for a biathlon. To train for the running portion of the race, she runs 7 miles each day over the same course. The first 4 miles of the course is on level ground, while the last 3 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? \n" ); document.write( "

Algebra.Com's Answer #671034 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = time in hrs to run on the downhill part
\n" ); document.write( " $\"+1+-+t+\"$ = time in hrs to run on level ground
\n" ); document.write( " $\"+s+\"$ = speed in mi/hr running downhill
\n" ); document.write( " $\"+s+-+3+\"$ = speed in mi/hr running on level ground
\n" ); document.write( "------------------------------------------------
\n" ); document.write( "Equation for funning on level ground:
\n" ); document.write( "(1) $\"+4+=+%28+s+-+3+%29%2A%28+1+-+t+%29+\"$
\n" ); document.write( "Equation for running downhill:
\n" ); document.write( "(2) $\"+3+=+s%2At+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "(2) $\"+t+=+3%2Fs+\"$
\n" ); document.write( "Plug (2) into (1)
\n" ); document.write( "(1) $\"+4+=+%28+s+-+3+%29%2A%28+1+-+3%2Fs+%29+\"$
\n" ); document.write( "(1) $\"+4+=+s+-+3+-+3+%2B+9%2Fs+\"$
\n" ); document.write( "(1) $\"+10+=+s+%2B+9%2Fs+\"$
\n" ); document.write( "Multiply both sides by $\"+s+\"$
\n" ); document.write( "(1) $\"+10s+=+s%5E2+%2B+9+\"$
\n" ); document.write( "(1) $\"+s%5E2+-+10s+%2B+9+=+0+\"$
\n" ); document.write( "(1) $\"+%28+s+-+9+%29%2A%28+s+-+1+%29+=+0+\"$ ( by looking at it )
\n" ); document.write( "I have to choose between
\n" ); document.write( " $\"+s+=+9+\"$ and
\n" ); document.write( " $\"+s+=+1+\"$
\n" ); document.write( "it can't be $\"+s+=+1+\"$ since
\n" ); document.write( " $\"+s+-+3+\"$ = speed in mi/hr running on level ground
\n" ); document.write( "and I would end up with negative speed
\n" ); document.write( "So, $\"+s+=+9+\"$
\n" ); document.write( "-------------------------------------
\n" ); document.write( "She runs 9 mi/hr on the downhill part
\n" ); document.write( "-------------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+t+=+3%2Fs+\"$
\n" ); document.write( "(2) $\"+t+=+3%2F9+\"$
\n" ); document.write( "(2) $\"+t+=+1%2F3+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+4+=+%28+s+-+3+%29%2A%28+1+-+t+%29+\"$
\n" ); document.write( "(1) $\"+4+=+%28+9+-+3+%29%2A%28+1+-+t+%29+\"$
\n" ); document.write( "(1) $\"+4+=+6%2A%28+1+-+t+%29+\"$
\n" ); document.write( "(1) $\"+4+=+6+-+6t+\"$
\n" ); document.write( "(1) $\"+6t+=+6+-+4+\"$
\n" ); document.write( "(1) $\"+6t+=+2+\"$
\n" ); document.write( "(1) $\"+t+=+1%2F3+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );