document.write( "Question 205892: A cyclist travels 80km from Paris to Louvre at an average speed of x km/h. Find the time taken in term of x. On his return journey from Louvre to Paris, he decreases his average speed by 3km/h. Find the time taken on the return journey in terms of x. If the difference between the times is one hour 20 minutes, find the value of x. \n" ); document.write( "

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A cyclist travels 80km from Paris to Louvre at an average speed of x km/h. Find the time taken in term of x.
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\n" ); document.write( "t1 = 80/x hours
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\n" ); document.write( "On his return journey from Louvre to Paris, he decreases his average speed by 3km/h. Find the time taken on the return journey in terms of x.
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\n" ); document.write( "t2 = 80/(x-3) hours
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\n" ); document.write( "If the difference between the times is one hour 20 minutes, find the value of x.
\n" ); document.write( "t1-t2 = 4/3 hours
\n" ); document.write( "80/x - 80/(x-3) = 4/3
\n" ); document.write( "Multiply thru by x(x-3)*3
\n" ); document.write( "80*(x-3)*3 - 80x*3 = 4x*(x-3)
\n" ); document.write( "240x-720 - 240x = 4x^2-12x
\n" ); document.write( "4x^2-12x+720 = 0
\n" ); document.write( "x^2-3x+180 = 0
\n" ); document.write( "(x-15)*(x+12) = 0
\n" ); document.write( "x = -12 kph (Ignore)
\n" ); document.write( "x = 15 khp \n" ); document.write( "

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