rohan2345 wrote:

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)5/12 hrs

(B) 2 2/5 hrs

(C) 2 4/5 hrs

(D) 3 1/2 hrs

(E) 4 4/5 hrs

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.

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