document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201574>Question 1201574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average speed of a car over a certain distance is calculated by dividing the total distance travelled by the total time taken. Two towns A and B are 10km apart, a motorist travels from A to B at an average speed of 20km per hour and travels from B to A at an average 40km per hour.<BR>\n" );
document.write( "(a) Determine the average speed to the motorist for the two trips combined. (I.e. from A to B and back to B and back to A)<BR>\n" );
document.write( "(b) Determine the speed would the motorist have to average on the return trip from B to A to yield an overall speed of 30km per hour? Assume the motorist has averaged 20km per hour from A to B<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836016 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=836016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A to B = 20 km per hour.<BR>\n" );
document.write( "B to A = 40 km per hour.<BR>\n" );
document.write( "D from A to B and from B to A is equal to 10.<BR>\n" );
document.write( "rate * time = distance.<BR>\n" );
document.write( "let x = the time it takes to get from A to B.<BR>\n" );
document.write( "let y = the time it takes to get from B to A.<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "20x = 10<BR>\n" );
document.write( "40y = 10<BR>\n" );
document.write( "solve for x to get x = 1/2 hour.<BR>\n" );
document.write( "solve for y to get y = 1/4 hour.<BR>\n" );
document.write( "total time to get from A to B and from B to A is 1/2 + 1/4 = 3/4 of an hour.<BR>\n" );
document.write( "rate * time = distance becomes rate * 3/4 = 20<BR>\n" );
document.write( "solve for rate to get rate = 20 / (3/4) = 80/3 kmph.<BR>\n" );
document.write( "average speed is 80/3 kmph = 26 and 2/3 kilometers per hour.<BR>\n" );
document.write( "if you want the aveage speed to get from A to B and then from B to A, to be 30 kmph, then rate * time = distance becomes 30 * time = 20.<BR>\n" );
document.write( "solve for time to get time = 2/3 of an hour.<BR>\n" );
document.write( "since going from A to B still takes 1/2 hour, then you get:<BR>\n" );
document.write( "1/2 + y = 2/3 of an hour.<BR>\n" );
document.write( "solve for y to get:<BR>\n" );
document.write( "y = 2/3 - 1/2 = 4/6 - 3/6 = 1/6.<BR>\n" );
document.write( "going from A to be takes 1/2 hour and going from B to A would have to take 1/6 of an hour.<BR>\n" );
document.write( "since B to A is 10 km, you get rate * 1/6 = 10 which gets you rate = 60 kmph.<BR>\n" );
document.write( "to have the overall speed equal 30 kmph, A to B would be at 20 kmph and B to A would be at 60 kmph.<BR>\n" );
document.write( "20x = 10 becomes x = 1/2<BR>\n" );
document.write( "60y = 10 becomes y = 1/6<BR>\n" );
document.write( "1/2 + 1/6 = total time of 4/6 of an hour.<BR>\n" );
document.write( "rate * time = 20 becomes rate * 4/6 = 20<BR>\n" );
document.write( "solve for rate to get rate = 20/(4/6) = 20*6/4 = 30 kmph.<BR>\n" );
document.write( "average speed round trip is 30 kmph.<BR>\n" );
document.write( "answer to a is 80/3 kmph average for the round trip = 26 and 2/3 kmph.<BR>\n" );
document.write( "answer to b is average speed from B to A would have to be 60 kmph so that the overall round trip average is 30 kmph.<BR>\n" );
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