document.write( "Question 532533: Mr. Smith traveled between two cities that were 750 km apart. On the return trip, he increased his average rate of travel by 20 kph and made the trip in 10 hours less time. Find his rate of travel in each direction. \n" ); document.write( "
Algebra.Com's Answer #350877 by htmentor(1343)\"\" \"About 
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Mr. Smith traveled between two cities that were 750 km apart. On the return trip, he increased his average rate of travel by 20 kph and made the trip in 10 hours less time. Find his rate of travel in each direction.
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\n" ); document.write( "Let s = his speed on the outbound trip
\n" ); document.write( "Then s + 20 = his speed on the return trip
\n" ); document.write( "Let t = his travel time on the outbound trip
\n" ); document.write( "Then t - 10 = his travel time for the return trip
\n" ); document.write( "Given: d = 750
\n" ); document.write( "Since distance = speed x time, for the two trips we have
\n" ); document.write( "750 = s*t
\n" ); document.write( "750 = (s+20)(t-10)
\n" ); document.write( "Solve for t in the 1st equation, substitute in the 2nd:
\n" ); document.write( "750 = (s+20)(750/s-10)
\n" ); document.write( "Solve for s:
\n" ); document.write( "750 = 750 - 10s + 15000/s - 200
\n" ); document.write( "Simplify:
\n" ); document.write( "s^2 + 20s - 1500 = 0
\n" ); document.write( "Factor:
\n" ); document.write( "(s+50)(s-30) = 0
\n" ); document.write( "Take the positive solution, s = 30
\n" ); document.write( "So the rates are 30 kph and 50 kph \n" ); document.write( "
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