document.write( "Question 159082: During the first part of a canoe trip, covered 75 miles at a certain speed. He then traveled 18 mile at a speed that was 5 slower. If the total time for the canoe trip was 3 hr, what was his speed on each part of the trip? \n" ); document.write( "

Algebra.Com's Answer #117198 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
For the two parts of the trip:
\n" ); document.write( " $\"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( " $\"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"d%5B1%5D+=+75\"$ mi
\n" ); document.write( " $\"d%5B2%5D+=+18\"$ mi
\n" ); document.write( " $\"r%5B2%5D+=+r%5B1%5D+-+5\"$
\n" ); document.write( " $\"t%5B1%5D+%2B+t%5B2%5D+=+3\"$ hr
\n" ); document.write( " $\"t%5B2%5D+=+3+-+t%5B1%5D\"$ hr
\n" ); document.write( "-----------------------
\n" ); document.write( " $\"d%5B1%5D+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( " $\"75+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( "(1) $\"t%5B1%5D+=+75+%2F+r%5B1%5D\"$
\n" ); document.write( "and
\n" ); document.write( " $\"d%5B2%5D+=+r%5B2%5D%2At%5B2%5D\"$
\n" ); document.write( " $\"18+=+%28r%5B1%5D+-+5%29%2A%283+-+t%5B1%5D%29\"$
\n" ); document.write( " $\"18+=+3r%5B1%5D+-+15+-+r%5B1%5D%2At%5B1%5D+%2B+5t%281%29\"$
\n" ); document.write( "Note that $\"r%5B1%5D%2At%5B1%5D+=+75\"$ (given)
\n" ); document.write( " $\"18+=+3r%5B1%5D+-+15+-+75+%2B+5t%5B1%5D\"$
\n" ); document.write( " $\"3r%5B1%5D+%2B+5t%5B1%5D+=+108\"$
\n" ); document.write( "from (1)
\n" ); document.write( " $\"3r%5B1%5D+%2B+5%2A%2875%2Fr%5B1%5D%29+=+108\"$
\n" ); document.write( "multiply both sides by $\"r%5B1%5D\"$
\n" ); document.write( " $\"3%28r%5B1%5D%29%5E2+%2B+375+=+108r%5B1%5D\"$
\n" ); document.write( "subtract $\"108r%5B1%5D\"$ from both sides
\n" ); document.write( "divide both sides by $\"3\"$
\n" ); document.write( " $\"%28r%5B1%5D%29%5E2+-+36r%5B1%5D+%2B+125+=+0\"$
\n" ); document.write( "use the quadratic formula
\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( "where
\n" ); document.write( " $\"a+=+1\"$
\n" ); document.write( " $\"b+=+-36\"$
\n" ); document.write( " $\"c+=+125\"$
\n" ); document.write( " $\"r%5B1%5D+=+%28-%28-36%29+%2B-+sqrt%28+%28-36%29%5E2-4%2A1%2A125+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"r%5B1%5D+=+%2836+%2B-+sqrt%28+1296+-+500+%29%29+%2F+2+\"$
\n" ); document.write( " $\"r%5B1%5D+=+%2836+%2B-+sqrt%28796%29%29+%2F+2+\"$
\n" ); document.write( " $\"r%5B1%5D+=+%2836+%2B+28.21%29+%2F+2+\"$
\n" ); document.write( " $\"r%5B1%5D+=+%2836+-+28.21%29+%2F+2+\"$
\n" ); document.write( " $\"r%5B1%5D+=+64.21%2F2\"$
\n" ); document.write( " $\"r%5B1%5D+=+32.1\"$ mi/hr
\n" ); document.write( "Using the (-) sign, the other answer is
\n" ); document.write( " $\"r%5B1%5D+=+3.90\"$ mi/hr (makes no sense, too small)
\n" ); document.write( "---------------------
\n" ); document.write( "check the 1st answer:
\n" ); document.write( " $\"r%5B2%5D+=+r%5B1%5D+-+5\"$
\n" ); document.write( " $\"r%5B2%5D+=+27.1\"$ mi/hr
\n" ); document.write( "----------------------
\n" ); document.write( " $\"75+=+32.1%2At%5B1%5D\"$
\n" ); document.write( " $\"t%5B1%5D+=+2.34\"$ hr
\n" ); document.write( " $\"18+=+r%5B2%5D%2At%5B2%5D\"$
\n" ); document.write( " $\"18+=+27.1%2At%5B2%5D\"$
\n" ); document.write( " $\"t%5B2%5D+=+.664\"$ hr
\n" ); document.write( "----------------------
\n" ); document.write( "The total time for the trip must be $\"3\"$ hr
\n" ); document.write( " $\"t%5B1%5D+%2B+t%5B2%5D+=+3\"$
\n" ); document.write( " $\"2.34+%2B+.664+=+3\"$
\n" ); document.write( " $\"3.004+=+3\"$ close enough
\n" ); document.write( "The speed for the 1st part was 32.1 mi/hr
\n" ); document.write( "The speed for the 2nd part was 27.1 mi/hr \n" ); document.write( "

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