document.write( "Question 606583: A family drove 1080 miles to their vacation lodge. Because of increased traffic density, their average speed on the return trip was decreased by 6 miles per hour and the trip took 2 1/2 hours longer. Determine their average speed on the way to the lodge. \n" ); document.write( "
Algebra.Com's Answer #382116 by LisaJ(11)\"\" \"About 
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Define some variables:\r
\n" ); document.write( "\n" ); document.write( "Speed going to lodge = V1 mph
\n" ); document.write( "Travel time = T1 hours
\n" ); document.write( "Speed going home = (V1 - 6) mph
\n" ); document.write( "Time going home = (T1 + 2.5) hours
\n" ); document.write( "Distance = speed * time = 1080 miles\r
\n" ); document.write( "\n" ); document.write( "equation 1: V1 * T1 = 1080
\n" ); document.write( "equation 2: (V1 - 6) * (T1 + 2.5) = 1080 \r
\n" ); document.write( "\n" ); document.write( "Solve for V1 and T1:
\n" ); document.write( "From eq 1, T1 = 1080/V1
\n" ); document.write( "substitute this into eq 2:
\n" ); document.write( "(V1 - 6) * [(1080/v1) + 2.5] = 1080
\n" ); document.write( "Simplify this to get a quadratic for V1:
\n" ); document.write( "\"V1%5E2+-+6+V1+-+2592+=+0\"
\n" ); document.write( "Solve; v1 = 54 or -48. Only a positive answer makes sense.
\n" ); document.write( "V1 = 54 mph\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "T1 = 1080/54 = 20 hours.
\n" ); document.write( "V2 = V1 - 6 = 48 mph
\n" ); document.write( "T2 = 20 + 2.5 = 22.5 hours
\n" ); document.write( "48 mph * 22.5 hours = 1080 miles
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