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

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If two workers can assemble a car in 8 hours and a third worker [#permalink]

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New post 19 May 2017, 02:19
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E

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  25% (medium)

Question Stats:

73% (01:07) correct 27% (01:38) wrong based on 56 sessions

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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

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Re: If two workers can assemble a car in 8 hours and a third worker [#permalink]

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New post 19 May 2017, 02:29
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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


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)
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Re: If two workers can assemble a car in 8 hours and a third worker [#permalink]

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New post 19 May 2017, 03:22
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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
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If two workers can assemble a car in 8 hours and a third worker [#permalink]

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New post 20 May 2017, 07:41
1
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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Re: If two workers can assemble a car in 8 hours and a third worker [#permalink]

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New post 20 May 2017, 07:58
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


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) \(4 \frac{4}{5}\)
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Re: If two workers can assemble a car in 8 hours and a third worker [#permalink]

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New post 22 May 2017, 18:49
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


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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Re: If two workers can assemble a car in 8 hours and a third worker   [#permalink] 22 May 2017, 18:49
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