document.write( "Question 92503: Scenario:
\n" ); document.write( "You need to make a round trip from Dallas to Ft. Worth (total distance 60 miles), and you want to average 60 miles an hour for your trip.\r
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\n" ); document.write( "\n" ); document.write( "Problem:
\n" ); document.write( "Traffic is heavy on the Dallas to Ft. Worth leg of your trip and you are only able to average 30 miles per hour
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\n" ); document.write( "How fast must you travel on the return leg in order to average 60 miles an hour for the entire trip?\r
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\n" ); document.write( "\n" ); document.write( "Ft. Worth to Dallas 30 miles
\n" ); document.write( "Dallas to Ft. Worth 30 miles
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Algebra.Com's Answer #67339 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "You need to make a round trip from Dallas to Ft. Worth (total distance 60 miles), and you want to average 60 miles an hour for your trip.
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\n" ); document.write( "Problem:
\n" ); document.write( "Traffic is heavy on the Dallas to Ft. Worth leg of your trip and you are only able to average 30 miles per hour
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\n" ); document.write( "How fast must you travel on the return leg in order to average 60 miles an hour for the entire trip?
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\n" ); document.write( "Ft. Worth to Dallas 30 miles
\n" ); document.write( "Dallas to Ft. Worth 30 miles
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\n" ); document.write( "\n" ); document.write( "Wow! You're just going there, turn around and come back. Then why go? Just to burn gas? Haha! Just joking.\r
\n" ); document.write( "\n" ); document.write( "On the serious side:\r
\n" ); document.write( "\n" ); document.write( "This is impossible because to average 60 mph you must go the entire 60 miles in 1 hour. However if you went 30 miles at 30 mph you have already used up the WHOLE HOUR!!, and you would need to already be back in Dallas at the end of that hour, but instead you are only in Ft. Worth. You cannot possibly have gone 60 miles at the end of that hour if you have only gone 30 miles at the end of that hour.
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document.write( "But let's pretend we weren't smart enough to notice that\r\n" );
document.write( "it's impossible and tried to solve it anyway.\r\n" );
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document.write( "Make this DRT-chart (pronounced \"dirt\"-chart)\r\n" );
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document.write( "            DISTANCE   RATE   TIME\r\n" );
document.write( "D to FtW \r\n" );
document.write( "FtW to D                             \r\n" );
document.write( "                             \r\n" );
document.write( "\r\n" );
document.write( "Let's let x be the answer to the problem, that is, the \r\n" );
document.write( "rate at which he must travel to achieve the goal of \r\n" );
document.write( "having averaged 60 mph.\r\n" );
document.write( "\r\n" );
document.write( "            DISTANCE   RATE   TIME\r\n" );
document.write( "D to FtW                              \r\n" );
document.write( "FtW to D                 x          \r\n" );
document.write( "\r\n" );
document.write( "Now the slow rate he had to travel when going from \r\n" );
document.write( "D to FtW is 30 mph, so let's fill that in for the \r\n" );
document.write( "rate going\r\n" );
document.write( "\r\n" );
document.write( "            DISTANCE   RATE   TIME\r\n" );
document.write( "D to FtW                30           \r\n" );
document.write( "FtW to D                 x         \r\n" );
document.write( "\r\n" );
document.write( "Now we are told the two distances are 30 miles going \r\n" );
document.write( "and 30 miles coming. So fill in 30 for each of the \r\n" );
document.write( "distances:\r\n" );
document.write( "\r\n" );
document.write( "            DISTANCE   RATE   TIME\r\n" );
document.write( "D to FtW       30       30            \r\n" );
document.write( "FtW to D       30        x         \r\n" );
document.write( "\r\n" );
document.write( "Next use the formula \r\n" );
document.write( "to fill in the two times:\r\n" );
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document.write( "\r\n" );
document.write( "            DISTANCE   RATE   TIME\r\n" );
document.write( "D to FtW       30       30     \r\n" );
document.write( "FtW to D       30        x     \r\n" );
document.write( "\r\n" );
document.write( "Reducing the  to just 1\r\n" );
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document.write( "            DISTANCE   RATE   TIME\r\n" );
document.write( "D to FtW       30       30      1\r\n" );
document.write( "FtW to D       30        x     \r\n" );
document.write( "\r\n" );
document.write( "Now we use the formula\r\n" );
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document.write( "                TOTAL DISTANCE\r\n" );
document.write( "AVERAGE RATE = 覧覧覧覧覧覧覧覧\r\n" );
document.write( "                 TOTAL TIME\r\n" );
document.write( "\r\n" );
document.write( "To get the TOTAL DISTANCE, we add the two DISTANCEs, \r\n" );
document.write( "30 miles going + 30 miles coming and that = 60 miles.\r\n" );
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document.write( "To get the TOTAL TIME, we add the two TIMEs, 1 + \r\n" );
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document.write( "For the AVERAGE RATE we substitute 60 mph. \r\n" );
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document.write( "So the equation is:\r\n" );
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document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "Write the left side as a fraction with 1 denominator:\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( "Now we can cross-multiply and get\r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
document.write( "\r\n" );
document.write( " = \r\n" );
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document.write( "Divide both sides by 60\r\n" );
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document.write( " = \r\n" );
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document.write( "Subtract 1 from both sides:\r\n" );
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document.write( " = \r\n" );
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document.write( "Multiply both sides by x\r\n" );
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document.write( " = \r\n" );
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document.write( "I don't think those are equal, do you? Haha! I think\r\n" );
document.write( "60 is a lots bigger than 0.  So if this problem has \r\n" );
document.write( "a solution, then 60 must equal to 0.  But since 60 \r\n" );
document.write( "doesn't equal 0, there can't be any solution to the \r\n" );
document.write( "problem.\r\n" );
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document.write( "So that's what you have to do if you can't reason out \r\n" );
document.write( "that the 1-hour span of time, that he must have been \r\n" );
document.write( "able to go 60 miles in, had already passed, and he's\r\n" );
document.write( "only done 30 miles in it, so it's too late for him to \r\n" );
document.write( "average 60 mph on the round trip.\r\n" );
document.write( " \r\n" );
document.write( "Edwin

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