SOLUTION: Jack and Jill live at opposite ends of the same street. Jack wanted to deliver a box at Jill's house, and Jill wanted to leave some flowers at Jack's house. THey started at the sam

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Question 237757: Jack and Jill live at opposite ends of the same street. Jack wanted to deliver a box at Jill's house, and Jill wanted to leave some flowers at Jack's house. THey started at the same moment, each walking at a constant speed. They met the first time 300 meters from Jack's house. On their return trip, they met 400 meters from Jill's house. How long is the street?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Jack and Jill live at opposite ends of the same street.
Jack wanted to deliver a box at Jill's house, and Jill wanted to leave some flowers at Jack's house.
They started at the same moment, each walking at a constant speed.
They met the first time 300 meters from Jack's house.
On their return trip, they met 400 meters from Jill's house.
How long is the street?
:
Let d = length of the street
Jill>-----(d-300)------|*|-----300------< Jack
First meeting Jill walks (d-300m); Jack walks 300M
:
jack>-----------400---------|*|--(d-400)-< Jill
Second meeting:
Jack walks: d-300) + 400 = (d+100)
Jill walks: 300 + (d-400)= (d-100)
:
The ratio of their walking distances will be the same, write a ratio equation:
Jill%2Fjack:%28%28d-300%29%29%2F300 = %28%28d-100%29%29%2F%28%28d%2B100%29%29
Cross multiply
(d-300)(d+100) = 300(d-100)
d^2 - 200d - 30000 = 300d - 30000
:
d^2 - 200d - 300d - 30000 + 30000 = 0
:
d^2 - 500d = 0
Factor out d
d(d - 500) = 0
d = 500 meters is the length of the street