Loading and unloading nails

[neeti2711]

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

[regor60]

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 RA, RB and RC be the respective rates.

1= 6(RA+RB) > 6 minutes Therefore, RB=1/6 - RA

1=9(RB+RC) > 9 minutes

So, 1=9(1/6-RA+RC) > Therefore, RC=RA-1/18

When A is loading and C unloading, the following equation holds:

1=T(RA-RC)

Substituting RC=RA-1/18 into the above yields T=18 minutes, C

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Hi neeti2711,

This question can be solved in a couple of different ways (and they all require a certain amount of 'math work', so this question will likely take you at least 2-3 minutes to solve it regardless of how you approach it).

Here's a way to approach it that involves rates and TESTing VALUES.

We're told that it takes Machines A and B, working together, to fill the bin in 6 minutes. Conceptually, it's easiest if those 2 Machines have the same rate, so let's TEST:

Machine A = 12 minutes to fill the bin alone
Machine B = 12 minutes to fill the bin alone

Thus, in 6 minutes, each of them will fill half the bin.

Next, we're told that it takes Machines B and C, working together, to fill the bin in 9 minutes. Since we've set Machine B's rate, we have to mathematically determine Machine C's rate.

In 9 minutes, Machine B will fill 3/4 of the bin. Thus, in those 9 minutes, Machine C has to fill the other 1/4 of the bin.

9 minutes = (1/4)(Full)
36 minutes = Full

Machine C = 36 minutes to fill the bin alone

Now that we've established the rates for Machines A and C, we can calculate how long it takes to fill the bin when Machine A is FILLING the bin and Machine C is EMPTYING the bin.

In 1 minute, Machine A 'fills' 1/12 of the bin. In that same minute, Machine C 'empties' 1/36 of the bin...

1/12 - 1/36 =
3/36 - 1/36 =
2/36
1/18

Thus, every minute, 1/18 of the bin is filled. Knowing that, it takes 18 minutes to fill the bin under these conditions.

Final Answer:C

GMAT assassins aren't born, they're made,
Rich

[GMATGuruNY]

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.

[Jeff@TargetTestPrep]

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 the loading rate of machines A, B and C be a, b and c, respectively. (Notice that the unloading rate of these machines will be -a, -b and -c, respectively.) Since rate x time = work and if we consider the work as 1, then we have:

(a + b) x 6 = 1 and (b + c) x 9 = 1

That is,

a + b = 1/6 and b + c = 1/9

Now if we subtract these two equations, we have (a + b) - (b + c) = 1/6 - 1/9, or, a - c = 1/18.
Notice that a - c is the rate of machine A loading the bin and machine C simultaneously unloading it. So if we let the time (in minutes) be t, we have:

(a - c) x t = 1

Since a - c = 1/18, we can substitute 1/18 for a - c in the equation (a - c) x t = 1:

1/18 x t = 1

t = 18

Answer:C