SOLUTION: If a bus traveled 10km/h faster, it would take 2 hours less time to make a 315km trip. What is its speed? Thanks for any help:)

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: If a bus traveled 10km/h faster, it would take 2 hours less time to make a 315km trip. What is its speed? Thanks for any help:)      Log On


   

Question 536711: If a bus traveled 10km/h faster, it would take 2 hours less time to make a 315km trip. What is its speed?
Thanks for any help:)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If a bus traveled 10km/h faster, it would take 2 hours less time to make a 315km trip.
What is its speed?
:
Let s = the speed of the bus
then
(s+10) = the faster speed
:
Write time equation, time = dist/speed
:
Actual time - faster time = 2 hrs
315%2Fs - 315%2F%28%28s%2B10%29%29 = 2
multiply by s(s+10)
s(s+10)*315%2Fs - s(s+5)*315%2F%28%28s%2B10%29%29 = 2s(s+10)
Cancel the denominators and you have
315(s+10) - 315s = 2s^2 + 20s
315s + 3150 - 315s = 2s^2 + 20s
0 = 2s^2 + 20s - 3150
Simplify, divide by 2
s^2 + 10s - 1575 = 0
Factors to
(s+45)(s-35) = 0
The positive solution
s = 35 mph is the actual bus speed
:
:
Check this by finding the times at each speed
315/35 = 9 hrs
315/45 = 7 hrs