document.write( "Question 1150319: Miguel went on a bike ride of 24 miles. He realized that if he had gone 6 mph faster, he would have arrived 9 hours sooner. How fast did he actually ride? \n" ); document.write( "

Algebra.Com's Answer #771696 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+r+\"$ = his normal rate in mi/hr
\n" ); document.write( "Let $\"+t+\"$ = his normal time in hrs
\n" ); document.write( "-------------------------------------------
\n" ); document.write( "Normal rate:
\n" ); document.write( "(1) $\"+24+=+r%2At+\"$
\n" ); document.write( "Faster rate:
\n" ); document.write( "(2) $\"+24+=+%28+r+%2B+6+%29%2A%28+t+-+9+%29+\"$
\n" ); document.write( "------------------------------------
\n" ); document.write( "(1) $\"+t+=+24%2Fr+\"$
\n" ); document.write( "(2) $\"+24+=+%28+r+%2B+6+%29%2A%28+24%2Fr+-+9+%29+\"$
\n" ); document.write( "(2) $\"+24+=+24+%2B+144%2Fr+-+9r+-+54+\"$
\n" ); document.write( "(2) $\"+0+=+144%2Fr+-+9r+-+54+\"$
\n" ); document.write( "(2) $\"+144%2Fr+=+9r+%2B+54+\"$
\n" ); document.write( "(2) $\"+144+=+9r%5E2+%2B+54r+\"$
\n" ); document.write( "(2) $\"+16+=+r%5E2+%2B+6r+\"$
\n" ); document.write( "(2) $\"+r%5E2+%2B+6r+-+16+=+0+\"$
\n" ); document.write( "(2) $\"+%28+r+%2B+8+%29%2A%28+r+-+2+%29+=+0+\"$
\n" ); document.write( "(2) $\"+r+=+2+\"$ ( can't use the negative result )
\n" ); document.write( "His normal rate was 2 mi/hr
\n" ); document.write( "-------------------------------
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+24+=+r%2At+\"$
\n" ); document.write( "(1) $\"+24+=+2%2At+\"$
\n" ); document.write( "(1) $\"+t+=+12+\"$ hrs
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+24+=+%28+r+%2B+6+%29%2A%28+t+-+9+%29+\"$
\n" ); document.write( "(2) $\"+24+=+%28+2+%2B+6+%29%2A%28+t+-+9+%29+\"$
\n" ); document.write( "(2) $\"+24+=+8%2A%28+t+-+9+%29+\"$
\n" ); document.write( "(2) $\"+t+-+9+=+3+\"$
\n" ); document.write( "(2) $\"+t+=+12+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );