document.write( "Question 171699: Brenda and her husband Randy bicycled cross-country together.One morning,Brenda rode 30 miles.By traveling only 5 miles per hour faster and putting in one more hour,Randy covered twice the distance.Brenda covered.What was the speed of each cyclist? \n" ); document.write( "

Algebra.Com's Answer #126833 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"d+=+r%2At\"$ for both of them
\n" ); document.write( "For Brenda:
\n" ); document.write( "(1) $\"d%5Bb%5D+=+r%5Bb%5D%2At%5Bb%5D\"$
\n" ); document.write( "For Randy:
\n" ); document.write( "(2) $\"d%5Br%5D+=+r%5Br%5D%2At%5Br%5D\"$
\n" ); document.write( "-------------
\n" ); document.write( "Given is:
\n" ); document.write( " $\"d%5Bb%5D+=+30\"$
\n" ); document.write( " $\"d%5Br%5D+=+60\"$
\n" ); document.write( " $\"r%5Br%5D+=+r%5Bb%5D+%2B+5\"$
\n" ); document.write( " $\"t%5Br%5D+=+t%5Bb%5D+%2B+1\"$
\n" ); document.write( "-------------
\n" ); document.write( "Now I can rewrite (1) and (2)
\n" ); document.write( "(1) $\"30+=+r%5Bb%5D%2At%7Bb%5D\"$
\n" ); document.write( " $\"t%5Bb%5D+=+30%2Fr%5Bb%5D\"$
\n" ); document.write( "(2) $\"60+=+%28r%5Bb%5D+%2B+5%29%2A%28t%5Bb%5D+%2B+1%29\"$
\n" ); document.write( "(2) $\"60+=+%28r%5Bb%5D+%2B+5%29%28%2830%2Fr%5Bb%5D%29+%2B+1%29\"$
\n" ); document.write( "(2) $\"60+=+30+%2B+150%2Fr%5Bb%5D+%2B+r%5Bb%5D+%2B+5\"$
\n" ); document.write( "Multiply both sides by $\"r%5Bb%5D\"$
\n" ); document.write( "(2) $\"60r%5Bb%5D+=+35r%5Bb%5D+%2B+150+%2B+r%5Bb%5D%5E2\"$
\n" ); document.write( "(2) $\"r%5Bb%5D%5E2+-+25r%5Bb%5D+%2B+150+=+0\"$
\n" ); document.write( "Looking at this, I see $\"%28-15%29%2A%28-10%29+=+150\"$ and $\"-10+-15+=+-25\"$
\n" ); document.write( "(2) $\"%28r%5Bb%5D+-+15%29%28r%5Bb%5D+-+10%29+=+0\"$
\n" ); document.write( "This is true if either $\"r%5Bb%5D+=+10\"$ or $\"r%5Bb%5D+=+15\"$
\n" ); document.write( "If $\"r%5Bb%5D+=+10\"$ , then
\n" ); document.write( " $\"r%5Br%5D+=+r%5Bb%5D+%2B+5\"$
\n" ); document.write( " $\"r%5Br%5D+=+10+%2B+5\"$
\n" ); document.write( " $\"r%5Br%5D+=+15\"$
\n" ); document.write( "---------------
\n" ); document.write( " $\"t%5Bb%5D+=+30%2Fr%5Bb%5D\"$
\n" ); document.write( " $\"t%5Bb%5D+=+30%2F10\"$
\n" ); document.write( " $\"t%5Bb%5D+=+3\"$
\n" ); document.write( "---------------
\n" ); document.write( " $\"t%5Br%5D+=+t%5Bb%5D+%2B+1\"$
\n" ); document.write( " $\"t%5Br%5D+=+3+%2B+1\"$
\n" ); document.write( " $\"t%5Br%5D+=+4\"$
\n" ); document.write( "---------------
\n" ); document.write( "Putting this together,
\n" ); document.write( "For Brenda:
\n" ); document.write( "(1) $\"30+=+10%2A3\"$
\n" ); document.write( "For Randy:
\n" ); document.write( "(2) $\"60+=+15%2A4\"$
\n" ); document.write( "---------------
\n" ); document.write( "These answers work, but what if $\"r%5Bb%5D+=+15\"$ ?
\n" ); document.write( " $\"t%5Bb%5D+=+30%2Fr%5Bb%5D\"$
\n" ); document.write( " $\"t%5Bb%5D+=+30%2F15\"$
\n" ); document.write( " $\"t%5Bb%5D+=+2\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"r%5Br%5D+=+r%5Bb%5D+%2B+5\"$
\n" ); document.write( " $\"r%5Br%5D+=+15+%2B+5\"$
\n" ); document.write( " $\"r%5Br%5D+=+20\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"t%5Br%5D+=+t%5Bb%5D+%2B+1\"$
\n" ); document.write( " $\"t%5Br%5D+=+2+%2B+1\"$
\n" ); document.write( " $\"t%5Br%5D+=+3\"$
\n" ); document.write( "-----------------
\n" ); document.write( "Putting these together,
\n" ); document.write( "(1) $\"30+=+15%2A2\"$
\n" ); document.write( "For Randy:
\n" ); document.write( "(2) $\"60+=+20%2A3\"$
\n" ); document.write( "These answers work too, so
\n" ); document.write( "The speeds of the cyclists were either
\n" ); document.write( "(1) Brenda went 10 mi/hr and Randy went 15 mi/hr
\n" ); document.write( "(2) Brenda went 15 mi/hr and Randy went 20 mi/hr \n" ); document.write( "

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