SOLUTION: In a 60km bicycle race, a rider calculates that if he can increase his speed by 6km/h he will cut his time for the distance by 20minutes. What was his original speed?

Question 709710: In a 60km bicycle race, a rider calculates that if he can increase his speed by 6km/h he will cut his time for the distance by 20minutes. What was his original speed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In a 60km bicycle race, a rider calculates that if he can increase his speed by 6km/h he will cut his time for the distance by 20minutes. What was his original speed?
:
Change 20 min to 1/3 hr
:
Let s = original speed
then
(s+6) = increased speed
:
Write a time equation time = dist/speed
- =
multiply by 3s(s+6) to clear the denominators, resulting in:
3(s+6)(60) + 3s(60) = s(s+6)
180s + 1080 + 180s = s^2 + 6s
A quadratic equation from all this
s^2 + 6s - 1080 = 0
You can solve this using the quadratic formula if you enjoy that sort of thing. But this will factor to:
(s + 36)(s + 30) = 0
The positive solution is all we want here
s = 30 km/hr is the original speed
:
:
Check this by finding the actual times
60/30 = 2 hrs
60/36 = 1.67
-------------
differ: .33 hrs which is 20 min
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