SOLUTION: Bryan took a 4-mile walk. The second half of his walk he averaged 1 mile per hour less than the first half, and it took him 1/3 hour longer. What rate did he average on the first h

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Question 213850: Bryan took a 4-mile walk. The second half of his walk he averaged 1 mile per hour less than the first half, and it took him 1/3 hour longer. What rate did he average on the first half of the walk?
This question has confused me and i do not know how to set it up.
I know the total distance is 4 miles.
He averaged 1/3 hour more on the second half.
He walked 1 mile per hour less
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Bryan took a 4-mile walk.
The second half of his walk he averaged 1 mile per hour less than the first
half, and it took him 1/3 hour longer.
What rate did he average on the first half of the walk?
:
Let s = speed on the 1st 2 mi
then
(s-1) = speed on the last 2 mi
:
Write a time equation: Time = dist%2Fspeed
1st half time + 1/3 hr = 2nd half time
2%2Fs + 1%2F3 = 2%2F%28%28s-1%29%29
Multiply equation by 3s(s-1)
3(s-1)*2 + s(s-1) = 3s(2)
:
6s - 6 + s^2 - s = 6s
:
s^2 - s + 6s - 6s - 6 = 0
:
s^2 - s - 6 = 0
Factor
(s-3)(s+2) = 0
Positive solution
s = 3 mph speed on the 1st half
:
:
Check by finding the times
2/3 hr
2/2 - 1 hr; 1/3 hr difference