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

Another method is to use combined rates in Rate*Time=Work formula.

Add rate of first two workers to the third worker's rate*:

\(\frac{1}{8}\) +\(\frac{1}{12}\)= \(\frac{20}{96}\)

Work / rate = time**

Work = 1. 1 divided by \(\frac{20}{96}\) = \(\frac{96}{20}\), which is the time it would take for the three workers to assemble a car ==>

\(\frac{96}{20}\) = \(\frac{24}{5}\) = 5\(\frac{4}{5}\) Answer E


*I haven't seen the "add or subtract" fractions LCM shortcut discussed much here. If it is discussed on this forum, I can't find it. To add fractions:
For the numerator: add the numbers in the denominator
For the denominator: multiply the numbers in the denominator.
Example, \(\frac{1}{3}\) + \(\frac{1}{17}\)
Numerator, add: 17 + 3 = 20
Denominator, multiply 17 * 3 = 51
Sum therefore = \(\frac{20}{51}\)

To preempt the "this-is-too-simple-for-GMAT-club-posters" naysayers: if you've seen the shortcut for adding and subtracting fractions, great. I and my peers, despite honors and AP classes and many semesters' of math in college, were not taught it. Apparently Vedic mathematicians used it. Whatever the case, it saves a lot of time.

If you haven't seen the shortcut, go here https://www.youtube.com/watch?v=0xlUbVf0OsQ, or
here https://www.youtube.com/watch?v=GFGlgSfQ-Gk, or
here https://www.algebra.com/algebra/homework/NumericFractions/jgr45.lesson

**Speed and time are directly proportional (if one increases, the other decreases). When the constant is 1 (work here is 1), simply flip the rate fraction to get the time taken. Hope it helps.

Let the total work be 24 units

Efficiency of A & B is 3 units/hr
Efficiency of C is 2 units/hr

Combined efficiency of A , B and C is 5 units/hr

Time taken for the three of them to do the work is \(\frac{24}{5} = 4 \frac{4}{5}\)

Hence, the correct answer must be (E) \(4 \frac{4}{5}\)

We are given that the two workers can assemble a car in 2 hours. Thus, the rate of those 2 workers is 1/8. We are also given that a third worker can assemble the same car in 12 hours, and thus has a rate of 1/12. If the workers were to work together to assemble the car, their rate would be:

1/8 + 1/12 = 3/24 + 2/24 = 5/24.

Thus, the time it would take them to complete the job would be:

(5/24)(time) = 1

time = 1/(5/24) = 24/5 = 4 4/5 hours

Answer: E

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