document.write( "Question 712954: On a recent trip, Sarah's car traveled 20 mph faster on the first 120 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip. I used the distance = rate * time. \n" ); document.write( "
Algebra.Com's Answer #438229 by stanbon(75887)\"\" \"About 
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On a recent trip, Sarah's car traveled 20 mph faster on the first 120 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.
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\n" ); document.write( "1st leg of trip DATA:
\n" ); document.write( "distance = 120 miles ; rate = x+20 mph ; time = d/r = 120/(x+20) hrs
\n" ); document.write( "---------------------------------------------
\n" ); document.write( "2nd leg of the trip DATA:
\n" ); document.write( "distance = 80 miles ; rate = x mph ; time = d/r = 80/x hrs
\n" ); document.write( "-------
\n" ); document.write( "Equation:
\n" ); document.write( "time + time = 4 hrs
\n" ); document.write( "120/(x+20) + 80/x = 4
\n" ); document.write( "---
\n" ); document.write( "30/(x+20) + 20/x = 1
\n" ); document.write( "30x + 20(x+20) = x(x+20)
\n" ); document.write( "-----
\n" ); document.write( "30x + 20x + 400 = x^2 + 20x
\n" ); document.write( "----
\n" ); document.write( "x^2 -30x -400 = 0
\n" ); document.write( "----
\n" ); document.write( "x^2-40x+10x-400 = 0
\n" ); document.write( "x(x-40)+10(x-40) = 0
\n" ); document.write( "(x-40)(x+10) = 9
\n" ); document.write( "Positive solution:
\n" ); document.write( "x = 40 mph (rate on leg 2 of the trip)
\n" ); document.write( "x+20 = 60 mph (rate on leg 1 of the trip)
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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