document.write( "Question 662292: Felipe jogs for 9 miles and then walks another 9 miles. He jogs 4.5
\n" ); document.write( " miles per hour faster than he walks, and the entire distance of 18 miles takes 3 hours. Find the rate at which he walks and the rate at which he jogs. \n" ); document.write( "

Algebra.Com's Answer #412126 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+t+\"$ = his time spent jogging in hrs
\n" ); document.write( " $\"+3+-+t+\"$ = his time spent walking in hrs
\n" ); document.write( "Let $\"+w+\"$ = his speed walking in mi/hr
\n" ); document.write( " $\"+w+%2B+4.5+\"$ = his speed jogging
\n" ); document.write( "----------
\n" ); document.write( "Equation for jogging:
\n" ); document.write( "(1) $\"+9+=+%28+w+%2B+4.5+%29%2At+\"$
\n" ); document.write( "Equation for walking:
\n" ); document.write( "(2) $\"+9+=+w%2A%28+3+-+t+%29+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "(2) $\"+9+=+3w+-+w%2At+\"$
\n" ); document.write( "(2) $\"+w%2At+=+3w+-+9+\"$
\n" ); document.write( "(2) $\"+t+=+3+-+9%2Fw+\"$
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+9+=+%28+w+%2B+4.5+%29%2A%28+3+-+9%2Fw+%29++\"$
\n" ); document.write( "(1) $\"+9+=+3w+%2B+13.5+-+9+-+40.5%2Fw+\"$
\n" ); document.write( "(1) $\"+18+-+13.5+=+3w+-+40.5%2Fw+\"$
\n" ); document.write( "(1) $\"+4.5+=+3w+-+40.5%2Fw+\"$
\n" ); document.write( "(1) $\"+4.5w+=+3w%5E2+-+40.5+\"$
\n" ); document.write( "(1) $\"+3w%5E2+-+4.5w+-+40.5+=+0+\"$
\n" ); document.write( "(1) $\"+2w%5E2+-+3w+-+27+=+0+\"$
\n" ); document.write( "use quadratic formula
\n" ); document.write( " $\"+w+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A%28-27%29+%29%29++%2F+%282%2A2%29+\"$
\n" ); document.write( " $\"+w+=+%28+3+%2B-+sqrt%28+9+%2B+216+%29%29++%2F+4+\"$
\n" ); document.write( " $\"+w+=+%28+3+%2B-+sqrt%28+225+%29%29++%2F+4+\"$
\n" ); document.write( " $\"+w+=+%28+3+%2B+15%29++%2F+4+\"$
\n" ); document.write( " $\"+w+=+18%2F4+\"$
\n" ); document.write( " $\"+w+=+4.5+\"$ ( ignore negative root )
\n" ); document.write( " $\"+w+%2B+4.5+=+9+\"$
\n" ); document.write( "he walks 4.5 mi/hr and jogs 9 mi/hr
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+9+=+4.5%2A%28+3+-+t+%29+\"$
\n" ); document.write( "(2) $\"+9+=+13.5+-+4.5t+\"$
\n" ); document.write( "(2) $\"+4.5t+=+13.5+-+9+\"$
\n" ); document.write( "(2) $\"+4.5t+=+4.5+\"$
\n" ); document.write( " $\"+t+=+1+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+9+=+%28+4.5+%2B+4.5+%29%2At+\"$
\n" ); document.write( "(1) $\"+9+=+9t+\"$
\n" ); document.write( " $\"+t+=+1+\"$
\n" ); document.write( "OK\r
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