SOLUTION: The distance between city A and B is 28 km. Two hikers left from each city (One from city A to city B and the other from city B to city A) heading towards each other at the same sp

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Question 638031: The distance between city A and B is 28 km. Two hikers left from each city (One from city A to city B and the other from city B to city A) heading towards each other at the same speed. The hiker from city A rested for an hour after having walked 9 km and then continued at a speed greater than 1 km/hour than his previous speed, then rested again 4 km away from city B. There he met the hiker from city B, who walked at a constant speed without resting until the two met. What were the speeds of the two hikers?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The distance between city A and B is 28 km.
Two hikers left from each city (One from city A to city B and the other from
city B to city A) heading towards each other at the same speed.
The hiker from city A rested for an hour after having walked 9 km and then
continued at a speed greater than 1 km/hour than his previous speed, then
rested again 4 km away from city B.
There he met the hiker from city B, who walked at a constant speed without
resting until the two met.
What were the speeds of the two hikers?
:
Let s = speed of the two hikers
then
(s+1) = speed of the A after his 1 hr rest
:
Find the distance hiker A traveled after his rest, to meet B, 4 km from City B
28-9-4 = 15 km
:
Write a time equation; time = dist/speed
9%2Fs + 15%2F%28s%2B1%29 + 1 = 4%2Fs
:
9%2Fs + 15%2F%28s%2B1%29 = 4%2Fs - 1
:
%289%28s%2B1%29%2B15s%29%2F%28s%28s%2B1%29%29 = %284-s%29%2Fs
:
%289s%2B9%2B15s%29%2F%28s%28s%2B1%29%29 = %284-s%29%2Fs
:
%2824s%2B9%29%2F%28s%28s%2B1%29%29 = %284-s%29%2Fs
Multiply both sides by s
%2824s%2B9%29%2F%28%28s%2B1%29%29 = (4 - s)
24s + 9 = (s+1)(4-s)
FOIL the right side
24s + 9 = 4s - s^2 + 4 - s
24s + 9 = 3s - s^2 + 4
Combine on the left
s^2 + 24s - 3s + 9 - 4 = 0
s^2 + 21s + 5 = 0
Actually this equation has two negative solutions so the given scenario is not possible.
It seems unreasonable, to find a speed, where A travels 24 km (+ a rest),
while B travels 4 km