document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=66567>Question 66567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart? \r<BR>\n" );
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document.write( "Hint: This is different from problem #3, because we do not know the total distance. We do know that one car is 180 miles ahead of the other, so the slow car's distance can be represented by \" d \" and the distance of the fast car, which would be ahead, can be represented by \"d + 180.\" The time is the same again, and can be represented by \"t.\" This time we have two unknowns, so we need two equations, one for the fast car, and one for the slow car. Again we are using the basic formula d = rt , and substituting the values that are relevant to our situation. The equation for the slow car is: d = 55t. You write the equation for the fast car, and solve the system by substitution. Don't forget the units in your answer.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #47224 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=47224\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "I SUGGEST THAT YOU LEARN THE CONCEPT OF RELATIVE SPEED TO<BR>\n" );
document.write( "SOLVE PROBLEMS IN TIME AND DISTANCE .SEE 2 EXAMPLES BELOW FOR CONCEPT<BR>\n" );
document.write( "AND WORKING.<BR>\n" );
document.write( "SOLUTION OF YOUR PROBLEM<BR>\n" );
document.write( "Two cars leave town going in the same direction. One travels 55 mph and the other travels 65 mph How long will it take before they are 180 miles apart?<BR>\n" );
document.write( "RELATIVE SPEED =65-55=10 MPH.<BR>\n" );
document.write( "DISTANCE OF SEPERATION = 180<BR>\n" );
document.write( "TIME NEEDED =180/10=18 HRS.\r<BR>\n" );
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document.write( "QUESTION<BR>\n" );
document.write( "1.Martina leaves home at 9 A.M., bicycling at a rate of<BR>\n" );
document.write( "24mi/h. Two hours later, John leaves, driving at a<BR>\n" );
document.write( "rate of 48mi/h. At what time will JOhn catch up with<BR>\n" );
document.write( "Martina?\r<BR>\n" );
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document.write( "I have been trying to figure this out for several<BR>\n" );
document.write( "hours now. Is this a trick question, because I cannot<BR>\n" );
document.write( "figure it out. I know that distance= rate times time<BR>\n" );
document.write( "(d=r x t), but it doesn't give the distance. <BR>\n" );
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document.write( "ANSWER<BR>\n" );
document.write( "OK ..but you have to learn the concept of RELATIVE<BR>\n" );
document.write( "SPEED HERE to do the problem.let me explain the<BR>\n" );
document.write( "principle first before we solve your problem<BR>\n" );
document.write( "let us say there are 2 persons ..you and your friend<BR>\n" );
document.write( "martina..let us say you are at one place to start with<BR>\n" );
document.write( "at your home and both of you start at the same<BR>\n" );
document.write( "time.you walk at 4 mph(miles per hour)say and martina<BR>\n" );
document.write( "walks at 3 mph.now see what happens after 1 hr.using<BR>\n" );
document.write( "your formula d=r*t,you will be 4 miles away from your<BR>\n" );
document.write( "home and martina will be 3 miles away...after 2 hours<BR>\n" );
document.write( "the distances will be 8 and 6 miles<BR>\n" );
document.write( "respectively...like this though you started at the<BR>\n" );
document.write( "same time and at the same place that is zero distance<BR>\n" );
document.write( "between you and martina,your distance of seperation<BR>\n" );
document.write( "increased to 4-3=1 mile in 1 hour ,8-6=2 miles in 2<BR>\n" );
document.write( "hrs...and so on..so now you are ready to take this<BR>\n" );
document.write( "concept of relative speed ...relative speed between<BR>\n" );
document.write( "you and martina is 4 mph - 3 mph = 1mph.in this case<BR>\n" );
document.write( "as you are travelling in the same direction.so you<BR>\n" );
document.write( "shoud use this relative speed for r in your formula of<BR>\n" );
document.write( "d=r*t...ok..the d in this case is the distance of<BR>\n" );
document.write( "seperation between you and martina at the start .it<BR>\n" );
document.write( "may be zero as we assumed in this case or may not be<BR>\n" );
document.write( "zero as given in your problem.similarly you mave to<BR>\n" );
document.write( "adjust for difference in time of start...but the<BR>\n" );
document.write( "principle is same so procedure is<BR>\n" );
document.write( "1.use relative speed.. this will be difference in<BR>\n" );
document.write( "speeds if you are travelling in same direction.BUT IT<BR>\n" );
document.write( "WILL BE SUM OF THE SPEEDS IF YOU ARE TRAVELLING IN<BR>\n" );
document.write( "OPPOSITE DIRECTIONS.CAN YOU GUESS WHY?BECAUSE AS WE<BR>\n" );
document.write( "ANALYSED ABOVE EVERY HOUR YOU TWO ARE APPROACHING EACH<BR>\n" );
document.write( "OTHER (HERE OFCOURSE AT THE BEGINING YOU TWO WILL HAVE<BR>\n" );
document.write( "TO BE SEPERATED BY A CERTAIN DISTANCE)AND THE DISTANCE<BR>\n" );
document.write( "OF SEPERATION REDUCES BY THE SUM OF YOUR SPEEDS EVERY<BR>\n" );
document.write( "HOUR.<BR>\n" );
document.write( "2.find the difference in time of start if any and its<BR>\n" );
document.write( "effect on distance of seperation at the start.<BR>\n" );
document.write( "3find the distance of seperation at start using given<BR>\n" );
document.write( "data and time gap mentioned in 2.<BR>\n" );
document.write( "4.note the end criteria..and use your standard formula<BR>\n" );
document.write( "d=r*t to meet the end criteria using relative speed<BR>\n" );
document.write( "for r and difference in distance of seperation between<BR>\n" );
document.write( "start and end positions.<BR>\n" );
document.write( "now let us see your example...<BR>\n" );
document.write( "1.relative speed =48-24=24 mph=r<BR>\n" );
document.write( "2.difference in time of start =2 hrs.<BR>\n" );
document.write( "3.distance of seperation at the start = the head start<BR>\n" );
document.write( "martina got in 2 hrs cycling at 24 mph=2*24=48 miles..<BR>\n" );
document.write( "4.end criteria is that they meet at the end ..that is<BR>\n" );
document.write( "distance of seperation at the end is zero.so<BR>\n" );
document.write( "difference in distance of seperation from start to end<BR>\n" );
document.write( "..... =48-0=48=d<BR>\n" );
document.write( "so using d=r*t,we get 48=24*t..or..t=48/24=2 hrs. that<BR>\n" );
document.write( "is john will catch up with martina in 2 hrs from his<BR>\n" );
document.write( "time of start that is 11=00+2....that is 13=00 hrs.<BR>\n" );
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