document.write( "Question 494886: At their top speeds, Lance Armstrong can cycle 130 miles in the same time it took Maurice Garin to cycle 80 miles. This is because Armstrong's top speed is 10mph faster than Garin's. Find the top speed of each. \n" ); document.write( "

Algebra.Com's Answer #335849 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = Armstrong's top speed
\n" ); document.write( "Let $\"b\"$ = Garin's top speed
\n" ); document.write( "You need 2 motion equations:
\n" ); document.write( "Armstrong's:
\n" ); document.write( "(1) $\"+d%5Ba%5D+=+r%5Ba%5D%2At%5Ba%5D+\"$
\n" ); document.write( "Garin's:
\n" ); document.write( "(2) $\"+d%5Bg%5D+=+r%5Bg%5D%2At%5Bg%5D+\"$
\n" ); document.write( "----------------
\n" ); document.write( "given:
\n" ); document.write( " $\"+t%5Ba%5D+=+t%5Bg%5D+\"$ hrs ( call them both $\"t\"$ )
\n" ); document.write( " $\"+d%5Ba%5D+=+130+\"$ mi
\n" ); document.write( " $\"+d%5Bg%5D+=+80+\"$ mi
\n" ); document.write( " $\"+r%5Ba%5D+=+r%5Bg%5D+%2B+10+\"$ mi/hr
\n" ); document.write( " $\"+r%5Bg%5D+=+r%5Ba%5D+-+10+\"$ mi/hr
\n" ); document.write( "-------------
\n" ); document.write( "(1) $\"+130+=+r%5Ba%5D+%2At+\"$
\n" ); document.write( "(2) $\"+80+=+%28+r%5Ba%5D+-+10+%29%2At+\"$
\n" ); document.write( "From (1)
\n" ); document.write( "(1) $\"+t+=+130%2Fr%5Ba%5D+\"$
\n" ); document.write( "(2) $\"+80+=+%28+r%5Ba%5D+-+10+%29%2A%28130%2Fr%5Ba%5D%29+\"$
\n" ); document.write( "(2) $\"+80+=+130+-+1300+%2F+r%5Ba%5D+\"$
\n" ); document.write( "(2) $\"+80r%5Ba%5D+=+130r%5Ba%5D+-+1300+\"$
\n" ); document.write( "(2) $\"+50r%5Ba%5D+=+1300+\"$
\n" ); document.write( "(2) $\"+r%5Ba%5D+=+26+\"$ mi/hr
\n" ); document.write( "and,
\n" ); document.write( " $\"+r%5Bg%5D+=+r%5Ba%5D+-+10+\"$
\n" ); document.write( " $\"+r%5Bg%5D+=+16+\"$ mi/hr
\n" ); document.write( "Armstrong's top speed is 26 mi/hr
\n" ); document.write( "Garin's top speed is 16 mi/hr \n" ); document.write( "

\n" );