document.write( "Question 1031941: Gilda walks to the train station. If she walks at the rate of 3 mph, she misses her train by 7 minutes. However, if she walks at the rate of 4 mph, she reaches the station 5 minutes before the arrival of the train. Find the distance Gilda walks to the station. David knew he made a mistake when he calculated that Gilda walks 123 miles to the station.
\n" ); document.write( "Read through David's calculations:
\n" ); document.write( "Using d = rt, the distance is the same, but the rate and time are different.
\n" ); document.write( "If Gilda misses the train, it means the time t needs 7 more minutes so d = 3(t + 7).
\n" ); document.write( "If she gets to the station 5 minutes early means the time t can be 5 minutes less so d = 4(t - 5).
\n" ); document.write( "3(t + 7) = 4(t - 5)
\n" ); document.write( "3t + 21 = 4t - 20
\n" ); document.write( "t = 41
\n" ); document.write( "d = rt, so d = 3(41) = 123
\n" ); document.write( "Find David's mistake in his calculations. Explain his mistake and include the correct calculations and solutions in your answer.
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Algebra.Com's Answer #646620 by josgarithmetic(39620) $\"\"$ $\"About$

You can put this solution on YOUR website!
Try analyzing and solving the described problem without checking first what David did.\r
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document.write( "             speed           time        distance\r\n" );
document.write( "\r\n" );
document.write( "WALK          3                     d\r\n" );
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document.write( "FASTER        4                     d\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "Continue when that data makes sense to you.\r
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\n" ); document.write( "\n" ); document.write( " $\"system%283%28t%2B7%2F60%29=d%2C4%28t-1%2F12%29=d%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"3t%2B7%2A3%2F60=4t-4%2F12\"$
\n" ); document.write( " $\"3t%2B7%2F20=4t-1%2F3\"$
\n" ); document.write( " $\"7%2F20=t-1%2F3\"$
\n" ); document.write( " $\"t=7%2F20%2B1%2F3\"$
\n" ); document.write( " $\"t=21%2F60%2B20%2F60\"$
\n" ); document.write( " $\"highlight_green%28t=41%2F60%29\"$ meaning 41 minutes, the time from beginning the walk until train will leave.\r
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\n" ); document.write( "\n" ); document.write( " $\"d=4%2841%2F60-5%2F60%29\"$ , taking the second equation of the system.
\n" ); document.write( " $\"d=4%2836%2F60%29\"$
\n" ); document.write( " $\"d=36%2F15\"$
\n" ); document.write( " $\"d=18%2F5\"$
\n" ); document.write( " $\"highlight%28d=2%263%2F5%29\"$ ---------MILES\r
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\n" ); document.write( "\n" ); document.write( "You can clearly see that at least one of David's mistakes was to forget the accounting properly for time units. Seven minutes is $\"7%2F60\"$ hour, and 5 minutes is $\"5%2F60=1%2F12\"$ hour. \n" ); document.write( "

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