document.write( "Question 558016: Pat biked 1 mile in 3 minutes with the wind at her back, and then she returned in 4 minutes riding against the wind. What was the speed of wind? \n" ); document.write( "

Algebra.Com's Answer #362890 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+s+\"$ = her speed with no wind
\n" ); document.write( "Let $\"+w+\"$ = the wind speed
\n" ); document.write( " $\"+s+%2B+w+\"$ = biking speed with the wind
\n" ); document.write( " $\"+s+-+w+\"$ = biking speed against the wind
\n" ); document.write( "-------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+1+=+%28+s+%2B+w+%29%2A3+\"$
\n" ); document.write( "(2) $\"+1+=+%28+s+-+w+%29%2A4+\"$
\n" ); document.write( "-------------------
\n" ); document.write( "(1) $\"+1+=+3s+%2B+3w+\"$
\n" ); document.write( "(2) $\"+1+=+4s+-+4w+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"4\"$
\n" ); document.write( "and both sides of (2) by $\"3\"$
\n" ); document.write( "Then add the equations
\n" ); document.write( "(1) $\"+4+=+12s+%2B+12w+\"$
\n" ); document.write( "(2) $\"+3+=+12s+-+12w+\"$
\n" ); document.write( " $\"+7+=+24s+\"$
\n" ); document.write( " $\"+s+=+7%2F24+\"$ mi/min
\n" ); document.write( " $\"+7%2F24+\"$ mi/min x $\"+60+\"$ min/mi = $\"+17.5+\"$ mi/hr
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+1+=+3s+%2B+3w+\"$
\n" ); document.write( "(1) $\"+1+=+3%2A%287%2F24%29+%2B+3w+\"$
\n" ); document.write( "(1) $\"+3w+=+24%2F24+-+21%2F24+\"$
\n" ); document.write( "(1) $\"+3w+=+3%2F24+\"$
\n" ); document.write( "(1) $\"+w+=+1%2F24+\"$ mi/min
\n" ); document.write( " $\"+1%2F24+\"$ mi/min x $\"+60+\"$ min/hr = $\"+2.5+\"$ mi/hr
\n" ); document.write( "The wind speed was 2.5 mi/hr
\n" ); document.write( "check answer:
\n" ); document.write( "(1) $\"+1+=+%28+s+%2B+w+%29%2A%283%2F60%29+\"$ (note that $\"3\"$ min = $\"+3%2F60+\"$ hrs)
\n" ); document.write( "(1) $\"+1+=+%28+17.5+%2B+2.5+%29%2A%283%2F60%29+\"$
\n" ); document.write( "(1) $\"+1+=++20%2A%283%2F60%29+\"$
\n" ); document.write( "(1) $\"+1+=+60%2F60+\"$
\n" ); document.write( "(1) $\"+1+=+1+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+1+=+%28+s+-+w+%29%2A%284%2F60%29+\"$
\n" ); document.write( "(2) $\"+1+=+%28+17.5+-+2.5+%29%2A%284%2F60%29+\"$
\n" ); document.write( "(2) $\"+1+=+15%2A%284%2F60%29+\"$
\n" ); document.write( "(2) $\"+1+=+60%2F60+\"$
\n" ); document.write( "(2) $\"+1=+1+\"$
\n" ); document.write( "'OK \n" ); document.write( "

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