SOLUTION: 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 25mins,how

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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 25mins,how fast does Racheal run?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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%2F60 = 5%2F12 hrs
:
Write a time equation: Time = dist/speed
:
Run time + Ride time = 25 min
2%2Fr + 4.5%2F%28%28r%2B45%29%29 = 5%2F12
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