document.write( "Question 364791: While training for a biatholon race, Kevin covered a total distance of 9 km by swimmmiing for 45 min and running for 20 min. The next day he swam for 30 min and ran for 40 min, covering 14 km. Find his rates (in km/h) for swimming and running. (Assume these rates are constant.) \n" ); document.write( "

Algebra.Com's Answer #260094 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"s\"$ = his rate swimming in km/hr
\n" ); document.write( "Let $\"r\"$ = his rate running in km/hr
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"s%2A%283%2F4%29+%2B+r%2A%281%2F3%29+=+9\"$ km
\n" ); document.write( "(2) $\"s%2A%281%2F2%29+%2B+r%2A%282%2F3%29+=+14\"$ km
\n" ); document.write( "Multiply both sides of (1) by $\"12\"$
\n" ); document.write( "and both sides of (2) by $\"6\"$
\n" ); document.write( "(1) $\"9s+%2B+4r+=+108\"$
\n" ); document.write( "(2) $\"3s+%2B+4r+=+84\"$
\n" ); document.write( "Subtract (2) from (1)
\n" ); document.write( "(1) $\"9s+%2B+4r+=+108\"$
\n" ); document.write( "(2) $\"-3s+-+4r+=+-84\"$
\n" ); document.write( " $\"6s+=+24\"$
\n" ); document.write( " $\"s+=+4\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"3%2A4+%2B+4r+=+84\"$
\n" ); document.write( " $\"4r+=+84+-+12\"$
\n" ); document.write( " $\"4r+=+72\"$
\n" ); document.write( " $\"r+=+18\"$
\n" ); document.write( "He swims 4 km/hr and runs 18 km/hr \n" ); document.write( "

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