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One robot, working independently at a constant rate, can assemble a do

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One robot, working independently at a constant rate, can assemble a do  [#permalink]

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New post 08 Jul 2018, 21:43
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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

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One robot, working independently at a constant rate, can assemble a do  [#permalink]

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New post 08 Jul 2018, 21:56
Bunuel wrote:
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


If one robot can assemble a doghouse in 12 minutes, it can assemble 5 doghouses in an hour.

Each of the robots will be able to assemble 12.5 doghouses in \(\frac{5}{2}\) hours
Since we cannot have half a dog house built, each robot will build 12 doghouses in \(2\frac{1}{2}\) hours.

Therefore, 10 such identical robots will assemble \(12*10 =\) 120(Option C) doghouses in \(2\frac{1}{2}\) hours
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One robot, working independently at a constant rate, can assemble a do  [#permalink]

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New post 08 Jul 2018, 21:57
Total time is 2.5hrs = 150min.
One robot takes 12min to build one complete doghouse.
So, in 150 min it builds \frac{150}{12} robots = 12.5 doghouses.
So 10 robots working simultaneously can build 12.5*10 = 125 doghouses.
Hence option D 125
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Re: One robot, working independently at a constant rate, can assemble a do  [#permalink]

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New post 09 Jul 2018, 05:32

Solution



Given:
    • One robot, working independently at a constant rate, can assemble a doghouse in 12 minutes

To find:
    • 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 ½ hours

Approach and Working:
In 1 hour, one robot can assemble 60/15 = 5 doghouses
    • Hence, in 2 ½ hours, 1 robot can assemble = 5 * 2.5 = 12.5 doghouses = 12 doghouses (as 0.5 cannot be counted as 1 whole)
    • Then, in 2 ½ hours, 10 robots can assemble = 12 * 10 = 120

Hence, the correct answer is option C.

Answer: C
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Re: One robot, working independently at a constant rate, can assemble a do &nbs [#permalink] 09 Jul 2018, 05:32
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