Question 356862
Rachael runs 2 km to her bus stop and then rides 4.5 kms to school.
 On average the bus is 45 km/hr faster than Racheal's average running speed.
 If the entire trip takes 25 min, how fast does Rachael run?
:
Let r = R's running speed
then
(r+45) = Bus speed
:
Convert 25 min to hrs.  {{{25/60}}} = {{{5/12}}} hrs
:
Write a time equation: Time = dist/speed
:
Run time + Ride time = 25 min
{{{2/r}}} + {{{4.5/((r+45))}}} = {{{5/12}}}
multiply eq by 12r(r+45), results:
24(r+45) + 54r = 5r(r+45)
:
24r + 1080 + 54r = 5r^2 + 225r
:
78r + 1080 = 5r^2 + 225r
:
0 = 5r^2 + 225r - 78r - 1080
A quadratic equation
5r^2 + 147r - 1080 = 0
Find the positive solution for r using the quadratic formula
a=5; b=147; c=-1080