document.write( "Question 1058008: Two cyclists, 25 KM apart set out at the same time and meet in 50 minutes. Had they been cycling in the same direction the faster would have overtaken the slower in 5 hours. Find their cycling speeds. \n" ); document.write( "

Algebra.Com's Answer #673024 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
In both these cases, you can think of
\n" ); document.write( "it as one of the cyclists moving and the
\n" ); document.write( "other one standing still.
\n" ); document.write( "-----------------------------
\n" ); document.write( "When they are moving towards eachother,
\n" ); document.write( "the moving one moves at the sum of their speeds
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "When moving in the same direction, let $\"+d+\"$ =
\n" ); document.write( "the distance the slower one travels until the
\n" ); document.write( "faster one catches up.
\n" ); document.write( "Moving towards eachother:
\n" ); document.write( "(1) $\"+25+=+%28+s%5B1%5D+%2B+s%5B2%5D+%29%2A%28+50%2F60+%29+\"$
\n" ); document.write( "Moving in the same direction:
\n" ); document.write( "Slower one:
\n" ); document.write( "(2) $\"+d+=+s%5B2%5D%2A5+\"$
\n" ); document.write( "Faster one:
\n" ); document.write( "(3) $\"+d+%2B+25+=+s%5B1%5D%2A5+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(1) $\"+%286%2F5%29%2A25+=+s%5B1%5D+%2B+s%5B2%5D+\"$
\n" ); document.write( "(1) $\"+s%5B1%5D+%2B+s%5B2%5D+=+30+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+s%5B2%5D+=+%281%2F5%29%2Ad+\"$
\n" ); document.write( "(3) $\"+s%5B1%5D+=+%281%2F5%29%2Ad+%2B+5+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "plug (2) and (3) into (1)
\n" ); document.write( "(1) $\"+%281%2F5%29%2Ad+%2B+5+%2B+%281%2F5%29%2Ad+=+30+\"$
\n" ); document.write( "(1) $\"+d+%2B+25+%2B+d+=+150+\"$
\n" ); document.write( "(1) $\"+2d+=+125+\"$
\n" ); document.write( "(1) $\"+d+=+62.5+\"$
\n" ); document.write( "--------------------------------
\n" ); document.write( "(2) $\"+d+=+5%2As%5B2%5D+\"$
\n" ); document.write( "(2) $\"+62.5+=+5s%5B2%5D+\"$
\n" ); document.write( "(2) $\"+s%5B2%5D+=+12.5+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(3) $\"+s%5B1%5D+=+%281%2F5%29%2Ad+%2B+5+\"$
\n" ); document.write( "(3) $\"+s%5B1%5D+=+%281%2F5%29%2A62.5+%2B+5+\"$
\n" ); document.write( "(3) $\"+s%5B1%5D+=+12.5+%2B+5+\"$
\n" ); document.write( "(3) $\"+s%5B1%5D+=+17.5+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "The faster one's speed is 17.5 km/hr
\n" ); document.write( "The slower one's speed is 12.5 km/hr
\n" ); document.write( "-----------------------------------
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+%286%2F5%29%2A25+=+s%5B1%5D+%2B+s%5B2%5D+\"$
\n" ); document.write( "(1) $\"+%286%2F5%29%2A25+=+17.5+%2B+12.5+\"$
\n" ); document.write( "(1) $\"+30+=+30+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "(2) $\"+d+=+s%5B2%5D%2A5+\"$
\n" ); document.write( "(2) $\"+d+=+12.5%2A5+\"$
\n" ); document.write( "(2) $\"+d+=+62.5+\"$ km
\n" ); document.write( "-----------------------
\n" ); document.write( "(3) $\"+d+%2B+25+=+s%5B1%5D%2A5+\"$
\n" ); document.write( "(3) $\"+d+%2B+25+=+17.5%2A5+\"$
\n" ); document.write( "(3) $\"+d+=+87.5+-+25+\"$
\n" ); document.write( "(3) $\"+d+=+62.5+\"$ km
\n" ); document.write( "-----------------------
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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