document.write( "Question 235021: A dreaded word problem. This is out of the Algebra textbook 5th edition by Dugopolski. Chapter 8.3 page 550 #85. Here's the problem:
\n" ); document.write( "Erin was traveling across the desert on her bicycle. Before lunch she traveled 60 miles (mi); after lunch she traveled 46 miles. She put in 1 hour more after lunch than before lunch, but her speed was 4 mph slower than before. What was her speed before lunch and after lunch?\r
\n" ); document.write( "\n" ); document.write( "The answer is in the back of the book, and it is:
\n" ); document.write( "Before -5 + the square root of (265) or 11.3 mph;
\n" ); document.write( "After -9 + the square root of (265) or 7.3 mph\r
\n" ); document.write( "\n" ); document.write( "We are just completely confused about how to get the solution. We attempted to set it up in a distance=rate*time chart, but are not having any luck with that. Could you please show how to get a solution to this problem? Thank you very much in advance!!
\n" ); document.write( "Sandy :-) \n" ); document.write( "

Algebra.Com's Answer #173224 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
You need 2 equations, 1 for each part 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( " $\"d%5B1%5D+=+60\"$ mi
\n" ); document.write( " $\"d%5B2%5D+=+46\"$ mi
\n" ); document.write( " $\"t%5B2%5D+=+t%5B1%5D+%2B+1\"$ hrs
\n" ); document.write( " $\"r%5B2%5D+=+r%5B1%5D+-+4\"$ mi/hr
\n" ); document.write( "----------------------
\n" ); document.write( "Now I can rewrite the equations
\n" ); document.write( "(1) $\"60+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( "(2) $\"46+=+%28r%5B1%5D+-+4%29%2A%28t%5B1%5D+%2B+1%29\"$
\n" ); document.write( "This is 2 equations and 2 unknowns, so it's solvable
\n" ); document.write( "(2) $\"46+=+r%5B1%5D%2At%5B1%5D+-+4t%5B1%5D+%2B+r%5B1%5D+-+4\"$
\n" ); document.write( "And, since $\"60+=+r%5B1%5D%2At%5B1%5D\"$ ,
\n" ); document.write( "(2) $\"46+=+60+-+4t%5B1%5D+%2B+r%5B1%5D+-+4\"$
\n" ); document.write( "(2) $\"r%5B1%5D+-+4t%5B1%5D+%2B+10+=+0\"$
\n" ); document.write( "Now go back to (1)
\n" ); document.write( "(1) $\"60+=+r%5B1%5D%2At%5B1%5D\"$
\n" ); document.write( " $\"t%5B1%5D+=+60%2Fr%5B1%5D\"$
\n" ); document.write( "plug this back into (2)
\n" ); document.write( "(2) $\"r%5B1%5D+-+4%2A%2860%2Fr%5B1%5D%29+%2B+10+=+0\"$
\n" ); document.write( "Multiply both sides by $\"r%5B1%5D\"$
\n" ); document.write( " $\"r%5B1%5D%5E2+-+240+%2B+10r%5B1%5D+=+0\"$
\n" ); document.write( " $\"r%5B1%5D%5E2+%2B+10r%5B1%5D+-+240+=+0\"$
\n" ); document.write( "This can be solved by completing the square
\n" ); document.write( " $\"r%5B1%5D%5E2+%2B+10r%5B1%5D+%2B+%2810%2F2%29%5E2+=+240+%2B+%2810%2F2%29%5E2\"$
\n" ); document.write( " $\"r%5B1%5D%5E2+%2B+10r%5B1%5D+%2B+25+=+240+%2B+25+\"$
\n" ); document.write( "The left side is a perfect square
\n" ); document.write( " $\"%28r%5B1%5D+%2B+5%29%5E2+=+265\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"r%5B1%5D+%2B+5+=+sqrt%28265%29\"$
\n" ); document.write( " $\"r%5B1%5D+=+sqrt%28265%29+-+5\"$ mi/hr
\n" ); document.write( "And, since
\n" ); document.write( " $\"r%5B2%5D+=+r%5B1%5D+-+4\"$
\n" ); document.write( " $\"r%5B2%5D+=+sqrt%28265%29+-+5+-+4\"$
\n" ); document.write( " $\"r%5B2%5D+=+sqrt%28265%29+-+9\"$ mi/hr\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );