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

Question

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

Source:   Nova GMAT  
Difficulty Level:   550

nishantd88 · Answer

First 2 can do 1/8 of the work in 1 hour and the 3rd worker can do 1/12th of the work in 1 hr

So all three together can do 1/8+1/12 of the work in 1 hr. This comes to 5/24. This is the work done in 1 hour.

So total time taken will be 24 by 5 or 4 4/5.

Option (E)

amanvermagmat · Answer

One way of doing this is to take the amount of work a car requires as LCM of given times.
LCM of 8 & 12 = 24. So we assume a car requires 24 units of work.

First two workers can do = 24/8 = 3 units of work per hour
Third worker can do = 24/12 = 2 units of work per hour

All three workers combined can do = 3+2 = 5 units of work per hour

Thus, no of hours required = 24/5 = 4 4/5 hours

Hence answer is  E

generis · Answer

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.

Abhishek009 · Answer

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}

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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

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