document.write( "Question 522953: I am having a very hard time with understanding how to come up with an answer to this word problem. During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip? \n" ); document.write( "
Algebra.Com's Answer #347115 by stanbon(75887)\"\" \"About 
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During the first part of a trip, a canoeist travels 91 miles at a certain speed. The canoeist travels 21 miles on the second part of the trip at a speed 5 mph slower. The total time for the trip is 5 hrs. What was the speed on each part of the trip?
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\n" ); document.write( "1st part DATA:
\n" ); document.write( "distance = 91 miles ; rate = r mph ; time = d/r = 91/r hrs
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\n" ); document.write( "2nd part DATA:
\n" ); document.write( "distance = 21 miles ; rate = r-5 mph ; time = d/r = 21/(r-5) hrs\r
\n" ); document.write( "\n" ); document.write( "----------------
\n" ); document.write( "Equation:
\n" ); document.write( "time + time = 5 hrs
\n" ); document.write( "91/r + 21/(r-5) = 5
\n" ); document.write( "----
\n" ); document.write( "91(r-5) + 21r = 5r(r-5)
\n" ); document.write( "112r - 455 = 5r^2-25r
\n" ); document.write( "---
\n" ); document.write( "Rearrange:
\n" ); document.write( "5r^2 - 137r + 455 = 0
\n" ); document.write( "Positive solution:
\n" ); document.write( "r = 23.5331 mph (1st part speed)
\n" ); document.write( "r-5 = 18.5331 mph (2nd part speed)
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\n" ); document.write( "Cheers,
\n" ); document.write( "stan H.
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