Question 205971
A cyclist travels 80km from Paris to Louvre at an average speed of x km/h.
 Find the time taken in term of x.
f(x) = {{{80/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.
f(x) = {{{80/((x-3))}}}
 
If the difference between the times is one hour 20 minutes, find the value of x.
:
Write a time equation: 20 min = {{{1/3}}} hr
:
slow speed time - fast speed time = 20 min
{{{80/((x-3))}}} - {{{80/x}}} = {{{1/3}}}
multiply equation by 3x(x-3), results
3x(80) - 3(x-3)*80 = x(x-3)
:
240x - 240x + 720 = x^2 - 3x
Arrange as a quadratic equation
x^2 - 3x - 720 = 0
We have to use the quadratic formula here:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
in this problem a=1; b=-3; c=-720
{{{x = (-(-3) +- sqrt(-3^2 - 4 * 1* -720 ))/(2*1) }}}
:
{{{x = (3 +- sqrt(9 - (-2880) ))/2 }}}
:
{{{x = (3 +- sqrt(9 + 2880))/2 }}}
:
{{{x = (3 +- sqrt(2889))/2 }}}
We want the positive solution here:
x = {{{(3 + 53.6656)/2}}}
x = {{{56.6656/2}}}
x = 28.33 km/hr
:
;
Check solution, find the times
80/25.33 = 3.16 hrs
80/28.33 = 2.82
---------------
differs = .34 hr ~ 20 min