document.write( "Question 157291: Every day Tim drives to work. One Monday morning, with heavy traffic, Tim averaged 30 miles per hour on the way in, and 50 miles per hour on the way home. What was Tim’s average speed for the entire trip?\r
\n" ); document.write( "\n" ); document.write( "Is it possible to determine how far Tim drives to work? Explain.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #115926 by gonzo(654)\"\" \"About 
You can put this solution on YOUR website!
he traveled x miles at 30 mph and x miles at 50 mph for a total of 2x miles.
\n" ); document.write( "since his total time traveling there and back should equal to the sum of his total time getting there and his total time getting back, the equation becomes.
\n" ); document.write( "total time = (x/30 + x/50)
\n" ); document.write( "total time is also equal to 2x/y where 2x is the total distance there and back and y is the average speed for the total distance there and back.
\n" ); document.write( "2x/y must then equal (x/30 + x/50).
\n" ); document.write( "we solve the equation x/30 + x/50 = 2x/y.
\n" ); document.write( "we multiply both sides by y to get xy/30 + xy/50 = 2x.
\n" ); document.write( "we multiply both sides by 150 (common factor) to get 5xy + 3xy = 300x.
\n" ); document.write( "we divide both sides by common factor x to get 5y + 3y = 300
\n" ); document.write( "we combine like terms to get 8y = 300
\n" ); document.write( "we divide both sides by 8 to get y = 37.5
\n" ); document.write( "answer is good for any value of x because the x canceled out of the equation.
\n" ); document.write( "solving for 2 different values of x taken at random we get the following:
\n" ); document.write( "500/30 + 500/50 = 1000/37.5
\n" ); document.write( "becomes 16.6666.... + 10 = 26.6666.....
\n" ); document.write( "becomes 26.6666....... = 26.6666.......
\n" ); document.write( "ok for one value.
\n" ); document.write( "any other value could be 5000 (10 x original number.)
\n" ); document.write( "166.6666........ + 100 = 266.6666...........
\n" ); document.write( "266.6666........ = 266.6666.........
\n" ); document.write( "ok for another value.
\n" ); document.write( "any other value of x would also satisfy the equation.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );