document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054139>Question 1054139</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me to solve this problem.\r<BR>\n" );
document.write( "\n" );
document.write( "During a certain week, a small wind generator and a small hydro unit together produce 5880 kWh, with the wind generator operating only 85.0% of the time. During another week, the two units produce 6240 kWh, with the wind generator working 95.0% of the time and the hydro unit down 7.50 h for repairs. Assuming that each unit has a constant output when operating, find the number of kilowatts produced by each in 1.00 h.\r<BR>\n" );
document.write( "\n" );
document.write( "Do not round intermediate results. Round only final answers. Round to the nearest integer.\r<BR>\n" );
document.write( "\n" );
document.write( "wind generator:<BR>\n" );
document.write( "hydro unit: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #669373 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=669373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assuming that these operate 24 hours a day and that there are 7 days in a week, then the total number of hours each is up, if they are up 100% of the time, will be 7 * 24 = 168 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "based on that assumption.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "85% of the time will be .85 * 168 = 142.8 hours.<BR>\n" );
document.write( "95% of the time will be .95 * 168 = 159.6 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general formula is rate * time = quantity of work produced.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the quantity of work produces is in kilowatt hours.<BR>\n" );
document.write( "the time is in hours.<BR>\n" );
document.write( "the rate will be in kilowatt hours per hour.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let w = the rate of the wind generator.<BR>\n" );
document.write( "let h = the rate of the hydro unit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the first week, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "142.8 * w + 168 * h = 5880\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for the second week, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "159.6 * w + (168 - 7.5) * h = 6240.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this can be simplified to 159.6 * w + 160.5 * h = 6240\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they are:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "142.8 * w + 168 * h = 5880<BR>\n" );
document.write( "159.6 * w + 160.5 * h = 6240\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assuming that you know how to solve equations simultaneously, i'll jump to the answer to tell you that the simultaneous solution to these equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "w = 26.86084142 kilowatts per hour.<BR>\n" );
document.write( "h = 12.16828479 kilowatts per hour.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your solution is that the wind generator generates 27 kilowatts per hour and the hydro unit generates 12 kilowatts per hour.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i also solved this graphically as shown below.<BR>\n" );
document.write( "look for the intersection between the lines of the two equations.<BR>\n" );
document.write( "the coordinate point of the intersection confirms the solution.<BR>\n" );
document.write( "in the graph, x represents w and y represents h.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2016/102405.jpg\" alt=\"$$$\" </>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you can confirm the solution is correct, by replacing w with 26.86084142 and h with 12.16828479 in the following equations.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "142.8 * w + 168 * h = 5880<BR>\n" );
document.write( "159.6 * w + 160.5 * h = 6240\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if my assumptions about the number of hours in a week being equal to 168, then i believe this solution is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "check it out and see if you think that this is reasonable.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );