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If 6 workers can build 4 cars in 2 days, then how many days

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If 6 workers can build 4 cars in 2 days, then how many days

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If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars?

(A) 5/3
(B) 9/4
(C) 8/3
(D) 11/4
(E) 10/3

I'm confused how to set up the formulas here. Can any experts help?

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Hi ardz24,

We're told that 6 workers can build 4 cars in 2 days. We're asked for the number of days needed for 8 workers to build 6 cars.

In these types of 'Work' questions, it helps to think in terms of the TOTAL work needed to complete a task. Here, we have 6 workers who EACH work for 2 days. That would be...

(6 workers)(2 days of work each) = 12 worker-days of effort needed to build 4 cars. In other words...
(12 worker-days)/(4 cars) = 3 worker-days per car

Thus, 1 worker could build a car in 3 days
2 workers could build a car in 1.5 days
3 workers could build a car in 1 day
Etc.

We're asked for the number of days it would take 8 workers to build 6 cars. The 6 cars would require....

(6 cars)(3 worker-days each) = 18 worker-days of effort
With 8 workers, the work required by EACH would be....
(18 worker-days of effort)/(8 workers) = 18/8 = 9/4 total days

Final Answer: B

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To use the rate formula, we can go through a process like this:

We know that our rate formula is 1/A + 1/B = 1/A and B, where A is the amount of time worker A takes to finish a job alone, B is the amount of time worker B takes to finish a job alone, and A and B is the amount of time workers A and B take to finish a job together. We can use this formula for as many workers as we want. Here, we have six workers, so we use the equation 1/A + 1/B + 1/C + 1/D + 1/E + 1/F = 1/A, B, C, D, E, and F.

We know that the six workers build 4 cars in 2 days. This also means that they build 1 car in 1/2 days. So we'll fill in 1/2 for A, B, C, D, E, and F:
1/A + 1/B + 1/C + 1/D + 1/E + 1/F = 1/(1/2)

We assume that all individual workers work at the same pace, so we'll call the number of days it takes for a single worker to build 1 car x:
1/x + 1/x + 1/x + 1/x + 1/x + 1/x = 2
6/x = 2

Now we solve for x:
x = 2

So we know it takes a single worker 3 days to build 1 car. Let's set up an equation for how long it would take 8 workers to build one car:
8(1/3) = 1/A, B, C, D, E, F, G, and H

Now we solve for the number of days is would take 8 workers to build one car:
8/3 = 1/A, B, C, D, E, F, G, and H
1/A, B, C, D, E, F, G, and H = 3/8

So it would take 8 workers 3/8 of a day to build 1 car. To find the number of days it would take to build 6 cars, we multiply by 6:
3/8 * 6 = 18/8 = 9/4

So it would take 8 workers 9/4 days to build 6 cars.

We can also go through this logically by understanding that time will be proportional to number of cars and inversely proportional to number of workers:

6 workers 4 cars = 2 days
1 worker 4 cars = 2 * 6 = 12 days
1 worker 1 car = 12 / 4 = 3 days
1 worker 6 cars = 3 * 6 = 18 days
8 workers 6 cars = 18 / 8 = 9/4 days

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ardz24 wrote:
If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars?

(A) 5/3
(B) 9/4
(C) 8/3
(D) 11/4
(E) 10/3
We can use the following equation:
(workers * days)/output = (workers * days)/output.

Since 6 workers take 2 days to produce 4 cars, and we must calculate the number of days for 8 workers to produce 6 cars, we get:
(6*2)/4 = (8x)/6
3 = 4x/3
9 = 4x
9/4 = x.

The correct answer is B.

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ardz24 wrote:
If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars?

(A) 5/3
(B) 9/4
(C) 8/3
(D) 11/4
(E) 10/3

I'm confused how to set up the formulas here. Can any experts help?
Another way to think about it: First, if 6 workers can do 4 cars in 2 days (or 2 cars in 1 day), we know they can do 6 cars in 3 days.

Next, know that Time and # of workers will have a reciprocal relationship. If we have twice as many workers, it will take 1/2 the time, etc. So if we have 8/6 as many workers, it will take them 6/8 the time.

If 6 workers could do 6 cars in 3 days, then 8 workers will do 6 cars in 6/8 the time, or (6/8) * 3 days = 9/4 days. The answer is B

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BTGmoderatorAT wrote:
If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars?

(A) 5/3
(B) 9/4
(C) 8/3
(D) 11/4
(E) 10/3
We know the rate of 6 workers is 4/2 = 2 cars/day. We can create a proportion to determine the rate of the 8 workers.

6/2 = 8/x

3 = 8/x

3x = 8

x = 8/3

Thus, it will take 8 workers 6/(8/3)= 18/8 = 9/4 days to build 6 cars.

Answer: B

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