Question 669481
 a man travels a total distance of 166km/hr.
 his average speed for the first 130km is xkm/hr and for the remaining journey, (x-25)km/hr.
if the whole journey takes 3 hours and 15 minutes, form an equation in terms of x.
:
Change 3 hrs 15 min to 3.25 hrs
:
Write a time equation; time = dist/speed
{{{130/x}}} + {{{36/((x-25))}}} = 3.25
Multiply by x(x-25), results
130(x-25) + 36x = 3.25x(x-25)
:
130x - 3250 + 36x = 3.25x^2 - 81.25x
:
166x - 3250 = 3.25x^2 - 81.25x
A quadratic equation
3.25x^2 - 81.25x - 166x + 3250 = 0
:
3.25x^2 - 247.25x + 3250 = 0
:
solve this equation 
Use the quadratic formula to find x;
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
 a=3.25, b=-247.25, c=3250
{{{x = (-(-247.25) +- sqrt(-247.25^2-4*3.25*3250 ))/(2*3.25) }}}
Do this rather tedious math, the reasonable solution x ~ 59.18 km/h 
;
find the time he would have saved if he maintains an average speed of xkm/hr throughout ? 
:
{{{166/59.18}}} = 2.8 hrs
3.25 - 2.8 = .45 hrs saved (.45*60 = 27 min)