document.write( "Question 1203653: Jay traveled from his house to his office at an average speed of 25mph. by traveling 5mph faster, he took 30 minutes less to return home. How far is Jay's office from his house \n" ); document.write( "

Algebra.Com's Answer #839394 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "You have received two responses showing a standard algebraic method for solving the problem.

\n" ); document.write( "Here is a solution using a very different method.

\n" ); document.write( "The two speeds are 25mph and 30mph, a ratio of 5:6.

\n" ); document.write( "Since the distances are the same, the ratio of times at the two speeds is 6:5.

\n" ); document.write( "The time at the higher speed is 1/2 hour less than the time at the lower speed.

\n" ); document.write( "x = hours at lower speed
\n" ); document.write( "x-1/2 = hours at higher speed

\n" ); document.write( "The ratio is 6:5

\n" ); document.write( " $\"x%2F%28x-%281%2F2%29%29=6%2F5\"$
\n" ); document.write( " $\"6%28x-%281%2F2%29%29=5x\"$
\n" ); document.write( " $\"6x-3=5x\"$
\n" ); document.write( " $\"x=3\"$

\n" ); document.write( "The time spent at the lower speed was 3 hours. Since the lower speed was 25mph, the distance was 3*25 = 75 miles.

\n" ); document.write( "ANSWER: 75 miles

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