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If two workers can assemble a car in 8 hours and a third worker can assemble ... ...

If two workers can assemble a car in 8 hours and a third worker can assemble the same car in 12 hours, then how long would it take the three workers together to assemble the car?

(A)

\frac{5}{12} hrs

(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set X: Word Problems

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Daniela Stevens

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Posted: 11/07/2012 09:10

Of the formula would be time= Work/rate, why divide 1/fraction work? Could you expolian further?

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Admin

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Posted: 11/13/2012 01:23

Hi Daniela,

This is a difficult and non-intuitive problem, so don't feel bad. Sometimes it's useful to spell it out using English:

Productivity rate of workers 1 and 2: 1 car per 8 hours, or 1/8 car per hour
Productivity rate of worker 3: 1 car per 12 hours, or 1/12 car per hour
The blended rate of workers 1&2 and worker 3 is (1/8 + 1/12) car per hour, or 5/24 car per hour. Hence, to assemble 1 car using the 3 workers, we need:

Productivity rate = # cars divided by time
5/24 = 1 divided by x hours
x = 1 divided by 5/24 = 24 / 5 = 4 4/5 hours

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