SOLUTION: 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 Ch

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?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
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