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If Sabrina can assemble a tank in 8 hours, and Janis can ass

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If Sabrina can assemble a tank in 8 hours, and Janis can ass [#permalink] New post 18 Jun 2018, 14:57
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Question Stats:

83% (01:10) correct 16% (00:34) wrong based on 12 sessions
If Sabrina can assemble a tank in 8 hours, and Janis can assemble a tank in 13 hours, then Sabrina and Janis working together at their constant respective rates can assemble a tank in approximately how many hours?

(A) 21
(B) 18
(C) 7
(D) 5
(E) 2
[Reveal] Spoiler: OA

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Re: If Sabrina can assemble a tank in 8 hours, and Janis can ass [#permalink] New post 23 Jun 2018, 10:58
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sandy wrote:
If Sabrina can assemble a tank in 8 hours, and Janis can assemble a tank in 13 hours, then Sabrina and Janis working together at their constant respective rates can assemble a tank in approximately how many hours?

(A) 21
(B) 18
(C) 7
(D) 5
(E) 2


Working together they can complete in = \(\frac{(Sabrina rate * Janis Rate)}{(Sabrina rate + Janis Rate)}\)
= \(\frac{(8 * 13)}{(8 + 13)}\) = \(\frac{104}{21}\) which nearly equal = 5. i.e. option D
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Re: If Sabrina can assemble a tank in 8 hours, and Janis can ass [#permalink] New post 24 Jun 2018, 16:58
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sandy wrote:
If Sabrina can assemble a tank in 8 hours, and Janis can assemble a tank in 13 hours, then Sabrina and Janis working together at their constant respective rates can assemble a tank in approximately how many hours?

(A) 21
(B) 18
(C) 7
(D) 5
(E) 2


The combined rate of both women is 1/8 + 1/13 = 13/104 + 8/104 = 21/104, so the time is 1/(21/104) = 104/21 hours, or approximately 5 hours.

Answer: D
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Re: If Sabrina can assemble a tank in 8 hours, and Janis can ass [#permalink] New post 25 Jun 2018, 07:39
Ans....D
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Re: If Sabrina can assemble a tank in 8 hours, and Janis can ass [#permalink] New post 10 Jul 2018, 05:36
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Explanation

Since Sabrina and Janis are working together, add their rates. Sabrina completes 1 tank in 8 hours, so she works at a rate of \(\frac{1}{8}\) tank per hour. Likewise, Janis works at a rate of \(\frac{1}{13}\) tank per hour. Now, add these fractions:

\(\frac{1}{8}+\frac{1}{13}=\frac{13}{104}+\frac{8}{104}=\frac{21}{104}\) tanks per hour, when working together.

Next, plug this combined rate into the W = RT formula to find the time. You might also notice that since the work is equal to 1, the time will just be the reciprocal of the rate:

Attachment:
image1.jpg
image1.jpg [ 39.37 KiB | Viewed 338 times ]


At this point, you do not need to do long division or break out the calculator! Just approximate: \(\frac{104}{21}\) is about 100 ÷ 20 = 5.

Alternatively, use some intuition to work the answer choices and avoid setting up this problem at all!

You can immediately eliminate (A) and (B), since these times exceed either worker’s individual time.

Also, since Sabrina is the faster worker, Janis’s contribution will be less than Sabrina’s. The two together won’t work twice as fast as Sabrina, but they will work more than twice as fast as Janis.

Therefore, the total time should be more than half of Sabrina’s individual time, and less than half of Janis’s individual time. 4 < t < 6.5, which leaves (D) as the only possible answer.
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Re: If Sabrina can assemble a tank in 8 hours, and Janis can ass   [#permalink] 10 Jul 2018, 05:36
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