document.write( "Question 1009262: Peggy competes in a biathlon by running and bicycling around a large loop through a city. She runs the loop one time and bicycles the loop five times. She can run 8 mph and she can ride 16 mph. If the total time it takes her to complete the race is 1 hr 45 min, determine the distance of the loop. \n" ); document.write( "

Algebra.Com's Answer #624755 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+t+\"$ = time in hrs for her to bicycle
\n" ); document.write( "5 times around the loop
\n" ); document.write( " $\"+1.75+-+t+\"$ = time in hrs for her to
\n" ); document.write( "run around loop 1 time
\n" ); document.write( "Let $\"+d+\"$ = the distance of the loop in miles
\n" ); document.write( "-------------------------------------
\n" ); document.write( "Her equation for running:
\n" ); document.write( "(1) $\"+d+=+8%2A%28+1.75+-+t+%29+\"$
\n" ); document.write( "Her equation for bicycling:
\n" ); document.write( "(2) $\"+5d+=+16t+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "(1) $\"+d+=+14+-+8t+\"$
\n" ); document.write( "Substitute (1) into (2)
\n" ); document.write( "(2) $\"+5%2A%28+14+-+8t+%29+=+16t+\"$
\n" ); document.write( "(2) $\"+70+-+40t+=+16t+\"$
\n" ); document.write( "(2) $\"+56t+=+70+\"$
\n" ); document.write( "(2) $\"+t+=+1.25+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "(2) $\"+5d+=+16t+\"$
\n" ); document.write( "(2) $\"+5d+=+16%2A1.25+\"$
\n" ); document.write( "(2) $\"+5d+=+20+\"$
\n" ); document.write( "(2) $\"+d+=+4+\"$
\n" ); document.write( "The distance of the loop is 4 mi
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+d+=+8%2A%28+1.75+-+t+%29+\"$
\n" ); document.write( "(1) $\"+d+=+8%2A%28+1.75+-1.25+%29+\"$
\n" ); document.write( "(1) $\"+d+=+8%2A.5+\"$
\n" ); document.write( "(1) $\"+d+=+4+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );