document.write( "Question 955979: Michael drove to work on Monday at 45 mph and arrived one minute early. The employee drove to work on Tuesday, leaving home at the same time driving 40 mph and arriving one minute late. How far does Michael live from work? What speed does he need to drive to arrive 5 minutes early? \n" ); document.write( "

Algebra.Com's Answer #854597 by n2(91) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Michael drove to work on Monday at 45 mph and arrived one minute early.
\n" ); document.write( "The employee drove to work on Tuesday, leaving home at the same time driving 40 mph and arriving one minute late.
\n" ); document.write( "How far does Michael live from work? What speed does he need to drive to arrive 5 minutes early?
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Let 'd' be the distance from home to work (the same as the returning distance), in miles.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The time Michael spent on Monday  was    hours  (the distance divided by the average speed).\r\n" );
document.write( "\r\n" );
document.write( "The time Michael spent on Tuesday was    hours  (the distance divided by the average speed).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "These two time intervals differ in 1 + 1 = 2 minutes.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, we write this \"time equation\"  \r\n" );
document.write( "\r\n" );
document.write( "     -  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve, multiply both sides by 40*45.  You will get\r\n" );
document.write( "\r\n" );
document.write( "    45d - 40d = \r\n" );
document.write( "\r\n" );
document.write( "       5d     =     60\r\n" );
document.write( "\r\n" );
document.write( "        d     =     60/5 = 12.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So. the distance from home to work is 12 miles.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus first question is answered.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To answer second question, calculate the travel time on Monday.  \r\n" );
document.write( "\r\n" );
document.write( "It is   of a hour, which is the same as   of an hour, or 16 minutes.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    +----------------------------------------------------------+\r\n" );
document.write( "    |    So, if Michaels leaves his home at the same time      |\r\n" );
document.write( "    |           every day (as the problem states),             |\r\n" );
document.write( "    |    he has 16+1 = 17 minutes to get the office on time.   |\r\n" );
document.write( "    +----------------------------------------------------------+\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To get the office 5 minutes earlier the control time, the travel time should be 17-5 = 12 minutes, or  of an hour.\r\n" );
document.write( "\r\n" );
document.write( "Hence, to get the office 5 minutes earlier the control time, his average speed should be   = 60 miles per hour.\r\n" );
document.write( "\r\n" );
document.write( "It is the answer to the second question.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved completely.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );