document.write( "Question 72137This question is from textbook Algebra and Trigonometry: Structure and Method
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document.write( ": Tim paddled his kayak 12km upstream against a 3km/h current and back again in 5 h 20 min. In that time how far could he have paddeld in still water? \n" );
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Algebra.Com's Answer #51599 by ankor@dixie-net.com(22740)![]() ![]() You can put this solution on YOUR website! Tim paddled his kayak 12km upstream against a 3km/h current, and back again in 5 h 20 min. In that time, how far could he have paddled in still water? \n" ); document.write( ": \n" ); document.write( "Here again we are given the total time so we will write a time equation: \n" ); document.write( ": \n" ); document.write( "Let s = speed in still water \n" ); document.write( "So we have: \n" ); document.write( "Speed with the current = (s+3) \n" ); document.write( "Speed against current = (s-3) \n" ); document.write( ": \n" ); document.write( "The one way distance is given as 12 km \n" ); document.write( ": \n" ); document.write( "The total time is given as 5 hr 20 min, we have to convert that to hrs only \n" ); document.write( "5 + 20/60 = 5 & 1/3 hrs, since we are dealing in fractions anyway let's call it \n" ); document.write( "(16/3) hrs \n" ); document.write( ": \n" ); document.write( "remember Time = Distance/speed \n" ); document.write( "upstream time + downstream time = 16/3 hrs \n" ); document.write( ": \n" ); document.write( " \n" ); document.write( ": \n" ); document.write( "A complicated common denominator 3(s-3)(s+3); but we can tough it out! \n" ); document.write( ": \n" ); document.write( "3(s+3)(12) + 3(s-3)(12) = 16(s-3)(s+3) \n" ); document.write( ": \n" ); document.write( "12(3s+9) + 12(3s-9) = 16(s^2 - 9) \n" ); document.write( ": \n" ); document.write( "36s + 108 + 36s - 108 = 16s^2 - 144 \n" ); document.write( ": \n" ); document.write( "72s = 16s^2 - 144 \n" ); document.write( ": \n" ); document.write( "arrange as a quadratic equation: \n" ); document.write( "16s^2 - 72s - 144 = 0 \n" ); document.write( ": \n" ); document.write( "Simplify, divide equation by 8: \n" ); document.write( "2s^2 - 9s - 18 = 0 \n" ); document.write( ": \n" ); document.write( "Factors to: \n" ); document.write( "(2s + 3)(s - 6) = 0 \n" ); document.write( ": \n" ); document.write( "2s = -3; ignore this solution: \n" ); document.write( "and \n" ); document.write( "s = +6 km/hr the speed in still water \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( "A quick check using the original equation: \n" ); document.write( "12/3 + 12/9 = \n" ); document.write( "4 + 4/3 = 5 & 1/3 hrs as given \n" ); document.write( ": \n" ); document.write( "But they said,\"In that time, how far could he have paddled in still water?\" \n" ); document.write( ": \n" ); document.write( "Remember: Distance = speed * time \n" ); document.write( "We have: 6 * 5 & 1/3 hr \n" ); document.write( "or \n" ); document.write( "6 * 16/3 = 96/3 = 32 km in 5 hr 20 min \n" ); document.write( ": \n" ); document.write( ": \n" ); document.write( " |