Question 927163
Al is 100 yards from Bill and Bill is 300 yards from Chuck.
 They all move to the right at constant speeds.
 In 6 minutes, Al overtakes Bill and in another 6 minutes, Al overtakes Chuck.
 How many minutes does it take Bill to overtake Chuck?
:
Let a = A's speed in yds/min
let b = B's speed
let c = C's speed
:
  A>------100yds-------B>--------------300yds--------------C>-------
:
Write a distance equation for each, dist = time * speed
A overtakes B in 6 min from start
6b + 100 = 6a
6b = 6a - 100
b = a - 16.67
A overtakes C in 12 min from start
12c + 400 = 12a
12c = 12a - 400
c  = a - 33.33
B overtakes C
Let t = time for this to happen
ct + 300 = bt
Replace c with (a-33.33), replace b with (a-16.67)
t(a-33.33) + 300 = t(a-16.67)
at - 33.33t + 300 = at - 16.67t
Subtract at from both sides
-33.33t + 300 = - 16.67t
300 = - 16.67t + 33.33t
300 = +16.67t
t = 300/16.67
t ~ 18 min for B to overtake C