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 August 11th, 2011, 10:49 PM #1 Newbie   Joined: Jun 2010 Posts: 24 Thanks: 0 Average speed problem A cyclist travels from Paris to the 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 3 km/h. Find the time taken in return journey in terms of x ? if the difference between the times is one hour 20 minutes, find the value of x ?
 August 11th, 2011, 11:14 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs Re: Average speed problem A cyclist travels from Paris to the Louvre at an average speed of x km/h. find the time taken in term of x ? Let d be the distance from Paris to the Louvre. $t_1=\frac{d}{x}$ On his return journey from the Louvre to Paris, he decreases his average speed by 3 km/h. Find the time taken in return journey in terms of x ? $t_2=\frac{d}{x-3}$ if the difference between the times is one hour 20 minutes, find the value of x ? $t_2-t_1=\frac{4}{3}=d$$\frac{1}{x-3}-\frac{1}{x}$$=\frac{3d}{x(x-3)}$ $4x(x-3)=9d$ $4x^2-12x-9d=0$ $x=\frac{12+\sqrt{144+144d}}{8}=\frac{3$$1+\sqrt{d+ 1}$$}{2}$

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