SOLUTION: In a 200 mile bike ride, Duva realized that if she could average 1 mile per hour faster than she did on her last 200 mile ride, she would finish 1 hour sooner. How long did she spe

Question 935389: In a 200 mile bike ride, Duva realized that if she could average 1 mile per hour faster than she did on her last 200 mile ride, she would finish 1 hour sooner. How long did she spend on her last 200 mile ride?
* Answer in minutes and round to the nearest 10 minutes.*
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
In a 200 mile bike ride, Duva realized that if she could average 1 mile per hour faster than she did on her last 200 mile ride, she would finish 1 hour sooner.
How long did she spend on her last 200 mile ride?
:
Find her speed first
Let s = her speed on the first 200 mi trip
then
(s+1) = her speed on the second
:
Write a time equation; time= dist/speed
1st trip time - 2nd trip time = 1 hr
- = 1
multiply equation by s(s+10, cancel the denominators and you have
200(s+1) - 200s = s(s+1)
200s + 200 - 200s = s^2 + s
Combine to make a quadratic equation on the right (200s's cancel)
0 = s^2 + s - 200
Use the quadratic formula, a=1, b=1, c=-200
I got a positive solution of
s = 13.651 mph for the 1st trip
:
Find the time for the 2nd trip (1 mph faster)
= 13.65 hrs
Find the time time in minutes
13.0651(60) = 819 ~ 820 minutes
:
:
Check this by finding the time of the 1st trip
= 14.65 hrs (1 hr longer)
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