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Two inlets P and Q are working on alternate hour for filling

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by GMATinsight » Thu Sep 27, 2018 9:48 pm

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Two inlets P and Q are working on alternate hour for filling an empty tank and only one inlet works at any point of time. How much time will it take to fill the tank completely?

1) Inlet P can fill the tank in 10 hours while working alone while Inlet Q takes 15 hours to fill the tank alone
2) Inlet P works for first hour to fill the tank

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Two inlets P and Q are working on alternate hour for filling

by fskilnik@GMATH » Wed Oct 03, 2018 2:16 pm
GMATinsight wrote:Two inlets P and Q are working on alternate hour for filling an empty tank and only one inlet works at any point of time. How much time will it take to fill the tank completely?

1) Inlet P can fill the tank in 10 hours while working alone while Inlet Q takes 15 hours to fill the tank alone
2) Inlet P works for the first hour to fill the tank

Source: www.GMATinsight.com
\[job\,\, = {\text{fill}}\,\,{\text{the}}\,\,{\text{tank}}\]
\[?\,\,\,:\,\,\,{\text{time}}\,\,\,{\text{for}}\,\,{\text{job}}\,\,\,\left( {{\text{1 - h}}\,\,{\text{alternating}}} \right)\]

(1) Let´s imagine one job is defined by 30 identical tasks (30 = LCM(10,15)). From this statement, we know that:

P does 3 tasks/h
Q does 2 tasks/h

In two hours 5 tasks are done, therefore in exactly 6*2 = 12 hours we have the job (6*5 = 30 tasks) done with P or Q starting!

Obs.: check this slightly different problem when you finish reading this one...
https://www.beatthegmat.com/two-inlets- ... tml#820621

(2) Insufficient:

If each inlet fills the tank in 2h, then ? equals 2h.
If each inlet fills the tank in 3h, then ? equals 3h.


The correct answer is therefore (A).

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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