document.write( "Question 979823: two hikers, Arione and Jairus, started from the same place
\n" ); document.write( "at the same time and walked towards Lipa City, which is 90
\n" ); document.write( "kilometers away from their place. Arione walked 1
\n" ); document.write( "kilometer per hour faster than Jairus and reached Lipa 1
\n" ); document.write( "hour before him. Find the rate of each hiker. \n" ); document.write( "
Algebra.Com's Answer #601073 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"+s+\" = Jairus's speed in km/hr
\n" ); document.write( "\"+s+%2B+1+\" = Arione's speed in km/hr
\n" ); document.write( "Let \"+t+%2B+1+\" = Jairus's time in hrs
\n" ); document.write( "\"+t+\" = Arione's time in hrs
\n" ); document.write( "---------------------------------
\n" ); document.write( "Jairus's equation:
\n" ); document.write( "(1) \"+90+=+s%2A%28+t%2B1+%29+\"
\n" ); document.write( "Arione's equation:
\n" ); document.write( "(2) \"+90+=+%28+s%2B1+%29%2At+\"
\n" ); document.write( "---------------------
\n" ); document.write( "(2) \"+s%2At+%2B+t+=+90+\"
\n" ); document.write( "and
\n" ); document.write( "(1) \"+s+=+90%2F%28+t+%2B+1+%29+\"
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) \"+%28+90%2F%28+t%2B1+%29+%29%2At+%2B+t+=+90+\"
\n" ); document.write( "Multiply both sides by \"+t%2B1+\"
\n" ); document.write( "(2) \"+90t+%2B+t%2A%28+t%2B1+%29+=+90%2A%28+t%2B1+%29+\"
\n" ); document.write( "(2) \"+90t+%2B+t%5E2+%2B+t+=+90t+%2B+90+\"
\n" ); document.write( "(2) \"+t%5E2+%2B+t+-+90+=+0+\"
\n" ); document.write( "I notice that \"+90+=+9%2A10+\", so
\n" ); document.write( "(2) \"+%28+t+%2B+10+%29%2A%28+t+-+9+%29+=+0+\"
\n" ); document.write( "\"+t+=+9+\" ( time must be positive )
\n" ); document.write( "and
\n" ); document.write( "(1) \"+90+=+s%2A%28+t%2B1+%29+\"
\n" ); document.write( "(1) \"+90+=+s%2A%28+9%2B1+%29+\"
\n" ); document.write( "(1) \"+90+=+10s+\"
\n" ); document.write( "(1) \"+s+=+9+\"
\n" ); document.write( "and
\n" ); document.write( "\"+s%2B1+=+10+\"
\n" ); document.write( "Ariones's rate is 10 km/hr
\n" ); document.write( "Jairus's rate is 9 km/hr
\n" ); document.write( "-----------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) \"+90+=+%28+s%2B1+%29%2At+\"
\n" ); document.write( "(2) \"+90+=+%28+9%2B1+%29%2A9+\"
\n" ); document.write( "(2) \"+90+=+90+\"
\n" ); document.write( "and
\n" ); document.write( "(1) \"+90+=+s%2A%28+t%2B1+%29+\"
\n" ); document.write( "(1) \"+90+=+9%2A%28+9%2B1+%29+\"
\n" ); document.write( "(1) \"+90+=+90+\"
\n" ); document.write( "OK\r
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\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
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