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? 
:
Let s = speed on the 1st 2 mi
then
(s-1) = speed on the last 2 mi
:
Write a time equation: Time = {{{dist/speed}}}
1st half time + 1/3 hr = 2nd half time
{{{2/s}}} + {{{1/3}}} = {{{2/((s-1))}}}
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