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One robot, working independently at a constant rate, can ass
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06 Jul 2018, 16:23
06 Jul 2018, 16:23
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Question Stats:
35% (01:34) correct
64% (01:33) wrong based on 97 sessions
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One robot, working independently at a constant rate, can assemble a doghouse in 12 minutes. What is the maximum number of complete doghouses that can be assembled by 10 such identical robots, each working on separate doghouses at the same rate for \(2\frac{1}{2}\) hours?
(A) 20
(B) 25
(C) 120
(D) 125
(E) 150
(A) 20
(B) 25
(C) 120
(D) 125
(E) 150
Re: One robot, working independently at a constant rate, can ass
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10 Jul 2018, 06:16
10 Jul 2018, 06:16
2
Expert Reply
Explanation
Note that choice (D) is a trap. This issue is relatively rare, but it’s worthwhile to be able to recognize it if you see it. In this case, each robot is independently assembling complete doghouses.
Since the question asks for the number of completed doghouses after \(2\frac{1}{2}\) hours, any incomplete doghouses must be removed from the calculations.
Since one robot completes a doghouse in 12 minutes, the individual hourly rate is 60 ÷ 12 = 5 doghouses per hour.
Therefore, each robot produces 5 × 2.5 = 12.5 doghouses in \(2\frac{1}{2}\) hours. (Or just divide the 150 total minutes by 12 minutes per doghouse to get the same result.)
However, the questions asks about completed doghouses, and the robots are working independently, so drop the decimal. Each robot completes only 12 complete doghouses in the time period, for a totalof 12 × 10 = 120 doghouses.
Note that choice (D) is a trap. This issue is relatively rare, but it’s worthwhile to be able to recognize it if you see it. In this case, each robot is independently assembling complete doghouses.
Since the question asks for the number of completed doghouses after \(2\frac{1}{2}\) hours, any incomplete doghouses must be removed from the calculations.
Since one robot completes a doghouse in 12 minutes, the individual hourly rate is 60 ÷ 12 = 5 doghouses per hour.
Therefore, each robot produces 5 × 2.5 = 12.5 doghouses in \(2\frac{1}{2}\) hours. (Or just divide the 150 total minutes by 12 minutes per doghouse to get the same result.)
However, the questions asks about completed doghouses, and the robots are working independently, so drop the decimal. Each robot completes only 12 complete doghouses in the time period, for a totalof 12 × 10 = 120 doghouses.
Re: One robot, working independently at a constant rate, can ass
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12 Aug 2018, 08:44
12 Aug 2018, 08:44
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This is simple=
We need complete dog houses - rate of complete dog hounses 60min/12 min( of single rate of robot) = 5
So 1 Hr= 5 dog houses 2hr 10 dog houses in 30min we get 30/12=2.5 BUT HERE we are not considering .5 because this is not complete.
so in 2.5 hrs one robot can make 12 dog houses so ---> so robots can make 12*10 =120 dog houses
Simple-
We need complete dog houses - rate of complete dog hounses 60min/12 min( of single rate of robot) = 5
So 1 Hr= 5 dog houses 2hr 10 dog houses in 30min we get 30/12=2.5 BUT HERE we are not considering .5 because this is not complete.
so in 2.5 hrs one robot can make 12 dog houses so ---> so robots can make 12*10 =120 dog houses
Simple-
