document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=171540>Question 171540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? \r<BR>\n" );
document.write( "\n" );
document.write( "2.	A business invests $10,000 in a savings account for two years.  At the beginning of the second year, an additional $3500 is invested.  At the end of the second year, the account balance is $15,569.75.  What was the annual interest rate? \r<BR>\n" );
document.write( "\n" );
document.write( "3.	Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. \r<BR>\n" );
document.write( "\n" );
document.write( "4.	The Hudson River flows at a rate of 3 miles per hour.  A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours.  What is the speed of the boat in still water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126700 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=126700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I will lay these out for you and you do the work<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1.the path is the same width all the way around the garden. In order to get the area of the path you need to take the garden plus the path area and subtract out the garden area. the garden plus path area is stated like this<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Length * Width = Area..(18+2x)(13+2x)where x is the width of the path<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Area of the garden is 18(13)=234.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "so putting it altogether we have (18+2x)(13+2x)-234=516.. you will have to use the quadratic formula<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2.10000(x+1)(x+1)+3500(x+1)=15569.75------>where x is the interest rate<BR>\n" );
document.write( "....again dealing with a quadratic formula.....<BR>\n" );
document.write( "3.d=rt........in both instances distance is equal<BR>\n" );
document.write( "lets call the rate of the slow trip r and time t<BR>\n" );
document.write( "lets call the rate of the fast trip r+10 and time(t-1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "so 200=rt...eq 1<BR>\n" );
document.write( "...200=(r+10)(t-1)..eq 2<BR>\n" );
document.write( ":change eq 1 to t=200/r and substitute it into eq 2 and solve for r...this will involves a quadratic equation again<BR>\n" );
document.write( ":<BR>\n" );
document.write( "4.Let s= speed of the boat in still water<BR>\n" );
document.write( "The current =3 mi/hr<BR>\n" );
document.write( "we know that d=rt or d/r=t for this problem we must break this up into 2 parts<BR>\n" );
document.write( "(distance upriver)/(rate going upriver)<BR>\n" );
document.write( "+ (distance downriver)/(rate going downriver) = 9 hrs<BR>\n" );
document.write( ":the we know the distance is 60 each way<BR>\n" );
document.write( "the rate going up stream is 60/s-3<BR>\n" );
document.write( "the rate going down stream is 60/s+3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "so we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28s-3%29%2B60%2F%28s%2B3%29=9 ALIGN=MIDDLE  ALT=\"60%2F%28s-3%29%2B60%2F%28s%2B3%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >again a quadratic equation<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "when you get the answers email them to me and I will let you know if they are correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );