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 894364: 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?
:
let s = his original speed
then
(s+6) = his faster speed
:
Change 20 min to hr
:
Write a time equation, time = dist/speed
slow time - fast time = 1/3 hr
- =
multiply eq by 3s(s+6) cancel the denominators and you have
3(s+6)*60 - 3s(60) = s(s+6)
60(3s+18) - 180s = s^2 + 6s
180s + 1080 - 180s = s^2 + 6s
combine like terms on the right, 180s is gone
0 = s^2 + 6s - 1080
Factors to
(s+36)(s-30) = 0
the positive solution
s = 30 mph is original speed
:
:
Confirm this find the time at each speed
60/30 = 2 hrs
60/36 = 1.67 hrs
----------------
diff .33 hrs which is 20 min
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