document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208878>Question 1208878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man calculates that if he continues at the present speed, to drive the remaining 100km of his trip, he will arrive 30 minutes late. In order to arrive on time, he must travel at an average rate of 10 kph faster. What is his present speed? </SPAN>\n" );
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document.write( "x = the man's current speed in kph<BR>\n" );
document.write( "y = time it takes to drive 100 km going at a speed of x kph\r<BR>\n" );
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document.write( "Let's consider the scenario where the man goes at his present speed.<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "100 km = (x kph)*(y hr)<BR>\n" );
document.write( "100 = xy<BR>\n" );
document.write( "y = 100/x<BR>\n" );
document.write( "This will be used to substitute in later.\r<BR>\n" );
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document.write( "Now consider when he goes 10 kph faster, so his travel duration is 30 minutes = 30/60 = 0.5 hours less. <BR>\n" );
document.write( "His old speed x is now x+10 kph.<BR>\n" );
document.write( "The old time duration y is now y-0.5 hours.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "100 = (x+10)*(y-0.5)<BR>\n" );
document.write( "100 = (x+10)*(100/x - 0.5) ........... replace y with 100/x\r<BR>\n" );
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document.write( "I'll let the student handle the scratch work from here.<BR>\n" );
document.write( "Solving for x should give x = -50 and x = 40. <BR>\n" );
document.write( "Ignore the negative solution because a negative speed makes no sense.\r<BR>\n" );
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document.write( "If the man travels at 40 kph, then he needs 100/40 = 2.5 hours to travel the 100 km.<BR>\n" );
document.write( "If he travels instead at 40+10 = 50 kph, then he needs 100/50 = 2 hours, which is 0.5 hrs = 30 min early compared to the 2.5 hour figure. This confirms we have the correct present speed.\r<BR>\n" );
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document.write( "Answer: <font color=red>40 kph</font><BR>\n" );
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document.write( " </SPAN>\n" );
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