Question 205967
Alphonse starts at point A and runs at a constant rate towards point C.
 At the same time, Brigitte starts at point B and runs towards point C also
 at a constant rate. 
They arrive at C at exactly the same moment. 
If they continue running in the same directions, Alphonse arrives at B 
exactly 10 seconds before Brigitte arrives at A. 
How fast was Brigitte running?


A|----60m------|C---40m----|B
:
Let a = Al's speed (in meters/sec)
Let b = Brig's speed
:
They arrive at C at the same time equation, 
{{{60/a}}} = {{{40/b}}}
cross multiply
40a = 60b
a = {{{(60b)/40}}}
a = 1.5b
:
Time for each running 100 meters equation
B's time = A's time + 10 sec
{{{100/b}}} = {{{100/a}}} + 10
:
Replace a with 1.5b
{{{100/b}}} = {{{100/(1.5b)}}} + 10
:
Multiply equation by 3 to get rid of the denominators, results
3(100) = 2(100) + 1.5b(10)
:
300 = 200 + 15b
:
300 - 200 = 15b
:
100 = 15b
b = {{{100/15}}}
b = 6{{{2/3}}} meters/sec is Brig's speed (that's 24 km/hr)
:
:
Check solution
Find A's speed: 1.5*6.667 ~ 10 meters/sec
Find the times
60/10 = 6 sec
40/6.667 ~ 6 sec