neeti2711 wrote:Machines A, B, and C can either load nails into a bin or unload nails from that bin. Each machine works at a constant rate that is the same for loading and for unloading, although the individual machines may have different rates. Working together to load at their respective constant rates, machines A and B can load the bin in 6 minutes. Likewise, working together to load at their respective constant rates, machines B and C can load the bin in 9 minutes. How long will it take machine A to load the bin if machine C is simultaneously unloading the bin?
a. 12 minutes
b. 15 minutes
c. 18 minutes
d. 36 minutes
e. 54 minutes
Let A = A's rate, B = B's rate, and C = C's rate.
Then:
The combined rate for A and B = A+B.
The combined rate for B and C = B+C.
Let the bin = 18 nails.
Since machines A and B together take 6 minutes to load the bin, A+B = w/t = 18/6 = 3 nails per minute.
Since machines B and C together take 9 minutes to load the bin, B+C = w/t = 18/9 = 2 nails per minute.
Subtracting B+C=2 from A+B=3, we get:
(A+B) - (B+C) = 3-2
A-C = 1 nail per minute.
Since A = the rate when A loads and -C = the rate when C
unloads, A-C = the rate when A loads and C unloads.
Since A-C = 1, the time to load the bin when A loads and C unloads = w/r = 18/1 = 18 minutes.
The correct answer is
C.
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