SOLUTION: 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 m

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 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 m      Log On


   

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.
solve this equation and hence find the time he would have saved if he maintains an average speed of xkm/hr throughout ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fx + 36%2F%28%28x-25%29%29 = 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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=3.25, b=-247.25, c=3250
x+=+%28-%28-247.25%29+%2B-+sqrt%28-247.25%5E2-4%2A3.25%2A3250+%29%29%2F%282%2A3.25%29+
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%2F59.18 = 2.8 hrs
3.25 - 2.8 = .45 hrs saved (.45*60 = 27 min)