document.write( "Question 320599: During the first part of a trip a conoeist travels 54 miles at a certain speed. The conoeist travels 8 miles on the second part of the trip at a speed 5mph slower. Total time of the trip is 3hrs. What was the speed of each part of the trip? \n" ); document.write( "
Algebra.Com's Answer #229608 by nyc_function(2741)\"\" \"About 
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\n" ); document.write( "Let x be the speed for the first part of the trip. So that part takes 54/x hours.
\n" ); document.write( "So the speed for the second part of the trip is x - 5, so that part takes 8/(x-5).
\n" ); document.write( "Therefore:
\n" ); document.write( "(54/x) + (8/(x-5)) = 3
\n" ); document.write( "54(x - 5) + 8x = 3x(x - 5)
\n" ); document.write( "54x - 270 + 8x = 3x^2 - 15x
\n" ); document.write( "62x - 270 = 3x^2 - 15x
\n" ); document.write( "3x^2 - 15x - 62x + 270 = 0
\n" ); document.write( "3x^2 - 77x + 270 = 0
\n" ); document.write( "x = (-(-77) +/- sqrt((-77)^2 - 4(3)(270))) / (2*3)
\n" ); document.write( "x = (77 +/- sqrt(5929 - 3240)) / 6
\n" ); document.write( "x = (77 +/- sqrt(2689)) / 6
\n" ); document.write( "x =~ 21.4759 or 4.19
\n" ); document.write( "If x =~ 4.19, then the speed for the first part of the trip is 4.19, and the speed for the second part of the trip is -0.81. But a negative number makes sense, so we'll discount that solution.
\n" ); document.write( "Therefore, x =~ 21.4759, so the speed for the first part of the trip is about 21.4759, so the speed for the second part of the trip is about 16.4759.\r
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