document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197436>Question 1197436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me in my assigments thankyouu!<BR>\n" );
document.write( "A car traveling at a uniform speed reached its destination which is 400 kilometers away from the city. On the return trip, because of motor trouble, the speed is reduced to 10 miles per hour. This caused the car to stay on the road 2 hours longer. Find the speed of car </SPAN>\n" );
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document.write( "I'll assume the part \"the speed is reduced to 10 miles per hour\" is supposed to be \"the speed is reduced <font color=red>by</font> 10 <font color=red>kilometers</font> per hour\".<BR>\n" );
document.write( "This way the units match up, and a speed of 10 mph or 10 kph seems way too slow for a car.<BR>\n" );
document.write( "If either of these assumptions are incorrect, then please let me know.\r<BR>\n" );
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document.write( "Let's organize what we know into a table<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD ></TD><TD >Distance (km)</TD><TD >Rate (kph)</TD><TD >Time (hr)</TD></tr><tr><TD >A to B</TD><TD >400</TD><TD >x</TD><TD >400/x</TD></tr><tr><TD >B to A</TD><TD >400</TD><TD >x-10</TD><TD >400/(x-10)</TD></tr>\n" );
document.write( "</TABLE>Distance = rate*time<BR>\n" );
document.write( "time = distance/rate\r<BR>\n" );
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document.write( "The time duration 400/(x-10) is larger since the speed x-10 is smaller compared to speed x.<BR>\n" );
document.write( "Subtracting the time durations will get us a 2 hour gap due to the phrasing \"This caused the car to stay on the road 2 hours longer\".\r<BR>\n" );
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document.write( "longerTime - shorterTime = 2 hour gap<BR>\n" );
document.write( "400/(x-10) - 400/x = 2\r<BR>\n" );
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document.write( "The first equation @josgarithmetic has set up is close, but the tutor has them incorrectly swapped.\r<BR>\n" );
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document.write( "Multiply both sides by x(x-10) and get everything to one side<BR>\n" );
document.write( "400/(x-10) - 400/x = 2<BR>\n" );
document.write( "x(x-10)(400/(x-10) - 400/x) = 2x(x-10)<BR>\n" );
document.write( "400x - 400(x-10) = 2x(x-10)<BR>\n" );
document.write( "400x - 400x+4000 = 2x^2-20x<BR>\n" );
document.write( "4000 = 2x^2-20x<BR>\n" );
document.write( "0 = 2x^2-20x-4000<BR>\n" );
document.write( "2x^2-20x-4000 = 0\r<BR>\n" );
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document.write( "Compare this to ax^2+bx+c = 0<BR>\n" );
document.write( "We find that<BR>\n" );
document.write( "a = 2<BR>\n" );
document.write( "b = -20<BR>\n" );
document.write( "c = -4000\r<BR>\n" );
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document.write( "Let's use the quadratic formula<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2820%2B-sqrt%28400%2B32000%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%2820%2B-sqrt%28400%2B32000%29%29%2F%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+50 ALIGN=MIDDLE  ALT=\"x+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-40 ALIGN=MIDDLE  ALT=\"x+=+-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The negative speed makes no sense, so we ignore it.\r<BR>\n" );
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document.write( "The only practical soluton is x = 50.\r<BR>\n" );
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document.write( "If x = 50, then x-10 = 50-10 = 40.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "If you travel 400 km at a speed of 50 kph, then you take 400/50 = 8 hours<BR>\n" );
document.write( "If you travel 400 km at a speed of 40 kph, then you take 400/40 = 10 hours<BR>\n" );
document.write( "There is a 10-8 = 2 hour gap between the durations, so our answers are confirmed.\r<BR>\n" );
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document.write( "Answers: <BR>\n" );
document.write( "On the way to the destination, the speed is <font color=red>50 kph</font> <BR>\n" );
document.write( "On the return trip, the speed is <font color=red>40 kph</font> <BR>\n" );
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