document.write( "Question 1124609: Courtney rides her bike then the bus and finally the train to visit her aunt. She rides her bike at 6 mph. The bus travels at 30 mph while the train carries her at 140 mph. She rides the train for 57 minutes less than she rides the bus. She traveled 363 miles in 5 hours 21 minutes. How long was she riding her bike and reading on the bus?
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Algebra.Com's Answer #740949 by ankor@dixie-net.com(22740)\"\" \"About 
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Courtney rides her bike then the bus and finally the train to visit her aunt.
\n" ); document.write( " She rides her bike at 6 mph.
\n" ); document.write( " The bus travels at 30 mph while the train carries her at 140 mph.
\n" ); document.write( " She rides the train for 57 minutes less than she rides the bus.
\n" ); document.write( " She traveled 363 miles in 5 hours 21 minutes.
\n" ); document.write( " How long was she riding her bike and riding on the bus?
\n" ); document.write( ":
\n" ); document.write( "change 5 hr 21 min to hrs: 5 + 21/60 = 5.35 hrs
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\n" ); document.write( "let b = time riding the bike
\n" ); document.write( "then
\n" ); document.write( "6b = distance on the bike
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\n" ); document.write( "let c = time riding the bus
\n" ); document.write( "then
\n" ); document.write( "30c = distance on the bus
\n" ); document.write( ":
\n" ); document.write( "let t = time on the train
\n" ); document.write( "then
\n" ); document.write( "140t = distance on the train
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\n" ); document.write( "total dist equation
\n" ); document.write( "6b + 30c + 140t = 363 mi
\n" ); document.write( ":
\n" ); document.write( "total time equation
\n" ); document.write( "b + c + t = 5.35
\n" ); document.write( ":
\n" ); document.write( "\"She rides the train for 57 minutes less than she rides the bus\"
\n" ); document.write( "c - 57 min = t
\n" ); document.write( "change 57 min to hrs: 57/60
\n" ); document.write( "c = t + .95
\n" ); document.write( ":
\n" ); document.write( "in the first equation replace c with (t+.95)
\n" ); document.write( "6b + 30(t+.95) + 140t = 363
\n" ); document.write( "6b + 30t + 28.5 + 140t = 363
\n" ); document.write( "6b + 170t = 363 - 28.5
\n" ); document.write( "6b + 170t = 334.5
\n" ); document.write( ":
\n" ); document.write( "Do the same in the 2nd equation
\n" ); document.write( "b + (t+.95) + t = 5.35
\n" ); document.write( "b + 2t = 5.35 - .95
\n" ); document.write( "b + 2t = 4.4
\n" ); document.write( "b = -2t + 4.4
\n" ); document.write( ":
\n" ); document.write( "Replace b with (-2t+4.4) in 6b + 170t = 334.5
\n" ); document.write( "6(-2t+4.4) + 170t = 334.5
\n" ); document.write( "-12t + 26.4 + 170t = 334.5
\n" ); document.write( "158t = 334.5 - 26.4
\n" ); document.write( "158t = 308.1
\n" ); document.write( "t = 308.1/158
\n" ); document.write( "t = 1.95 hrs on the train
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\n" ); document.write( "find how long on the bike
\n" ); document.write( "b = -2(1.95) + 4.4
\n" ); document.write( "b = 3.9 + 4.4
\n" ); document.write( "b = .5 hrs on the bike
\n" ); document.write( ":
\n" ); document.write( "Now how long on the bus
\n" ); document.write( ".5 + c + 1.95 = 5.35
\n" ); document.write( "c = 5.35 - 2.45
\n" ); document.write( "c = 2.9 hrs on the bus
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\n" ); document.write( "\"How long was she riding her bike and riding on the bus?
\n" ); document.write( ".5 hrs and 2.9 hrs, that is
\n" ); document.write( "30 min on the bike
\n" ); document.write( "2 hr 54 min on the bus
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\n" ); document.write( ":
\n" ); document.write( "These solutions were not integers so checked this using the matrix feature on my Ti83
\n" ); document.write( "1, 1, 1, 5.35
\n" ); document.write( "6, 30, 140, 363
\n" ); document.write( "0, 1 - 1, .95
\n" ); document.write( "It was gratifying to see that their solutions agreed with mine: .5, 2.9, 1.95
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