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 haftakhan August 11th, 2011 09:49 PM

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 ?

 MarkFL August 11th, 2011 10:14 PM

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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