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?
:
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/jack}}}:{{{((d-300))/300}}} = {{{((d-100))/((d+100))}}}
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