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One robot builds a robot in 1 hour, another one builds a robot in 2 ho

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dimri10
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One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  Updated on: 24 Apr 2015, 08:40
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One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 5 robots altogether, if the robots build only one robot at a time?

A. 70 min
B. 94 min
C. 110 min
D. 112 min
E. 120 min
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Originally posted by dimri10 on 13 Jun 2011, 01:39.
Last edited by Bunuel on 24 Apr 2015, 08:40, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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subhashghosh
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Re: One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  13 Jun 2011, 02:00
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First the 2 robots work at the rate of
1 + 1/2 = 3/2

so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)

Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1

so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)

Now the 4 robots work together at the rate of

1 + 1/2 + 1/2 + 1/2 = 5/2

so they complete one robot in 2/5th of an hour - (3)

And now we have 5 robots

So Total = (1) + (2) + (3) = 94 minutes

Answer - B
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dimri10
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Re: One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  13 Jun 2011, 02:17
well after seeing that simple approach it's seems not that hard. thank's-5 stars for the method
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Re: One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  13 Jun 2011, 23:15
3rd robot = 1+ 1/2 = 40 min
4th robot = 1+ 1/2+ 1/2 = 30 min
5th robot = 1+1/2+1/2+1/2 = 24 min.

initially 2 robots are present. thus total is 94.
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puneetj
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Re: One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  14 Jun 2011, 19:00
2 robots are already there..
3rd in 40 mins
4th in 30 mins
5th in 24 mins

Total = 94 mins
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JeffTargetTestPrep
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Re: One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  30 May 2018, 17:14
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dimri10 wrote:
One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 5 robots altogether, if the robots build only one robot at a time?

A. 70 min
B. 94 min
C. 110 min
D. 112 min
E. 120 min


The rate of the first robot is 1 and the rate of the second robot is 1/2. Thus it will take both of them 1/(1 + 1/2) = 1/(3/2) = 2/3 hour = 40 minutes to build a new robot.

Now we have 3 robots. Since the rate of this new robot (or any new robot) is 1/2, it will take the three of them 1/(1 + 1/2 + 1/2) = 1/2 hour = 30 minutes to build a new robot.

Now we have 4 robots and it will take the four of them 1/(1 + 1/2 + 1/2 + 1/2) = 1/(5/2) = 2/5 hour = 24 minutes to build a new robot.

Since now we have 5 robots, we see that it takes 40 + 30 + 24 = 94 minutes to have 5 (2 existing and 3 built) robots.

Answer: B
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Re: One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  16 Oct 2020, 12:05
Lets use the letters A-E to denote the 5 robots:

Rate of Robot A: 1
Rate of Robot A+B = 1 + 1/2 = 3/2
Time to build robot C = 2/3 (inverse of rate) = 40 minutes

Rate of Robot A+B+C = 3/2 + 1/2 = 4/2
Time to build robot D = 2/4 = 30 minutes

Rate of Robot A+B+C+D = 3/2 + 1/2 + 1/2 = 5/2
Time to build robot E = 2/5 = 24 minutes

40 minutes + 30 minutes + 24 minutes = 94 minutes.

Answer is B.
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ouslam
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Re: One robot builds a robot in 1 hour, another one builds a robot in 2 ho [#permalink] New post  17 Oct 2020, 00:08
The question can be made clearer if you add the information that every robot that is produced will work with the others (here it looks like only the second robot is actually joining , the rest is not )
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