document.write( "Question 408747: Liz drove the first half of a trip at 36 mi/h. At what speed should she cover the remaining half in order to average 45 mi/h for the whole trip? \n" ); document.write( "

Algebra.Com's Answer #287876 by robertb(5830) $\"\"$ $\"About$

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When you said \"first half of a trip \", did you mean with respect to time or with respect to distance?
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\n" ); document.write( "\n" ); document.write( "Okay.\r
\n" ); document.write( "\n" ); document.write( "Let d = total distance.
\n" ); document.write( "Then for d/2 miles at 36 mph, his time was (d/2)/36 = d/72.
\n" ); document.write( "For the remaining d/2 miles at r mph, his time was (d/2)/r = d/(2r).
\n" ); document.write( "Total time of travel is $\"d%2F72+%2B+d%2F%282r%29\"$ hours.
\n" ); document.write( "Then we want $\"d%2F%28d%2F72+%2B+d%2F%282r%29%29+=+45\"$
\n" ); document.write( "<==> $\"1%2F%281%2F72+%2B+1%2F%282r%29%29+=+45\"$ <==> $\"1%2F72+%2B+1%2F%282r%29+=+1%2F45\"$
\n" ); document.write( "==> $\"1%2F%282r%29+=+1%2F120\"$ ==> r = 60 mph, his rate at the 2nd half of the trip. \n" ); document.write( "

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