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

Question

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

pushpitkc · Accepted Answer

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

Disillusioned · Answer

Most important take away from this questions:
- Not to multiply the number of robots / workers in the beginning
- Calculate work done by single robot for requested time, then multiply the number of robots to get the work done for all of them.

GoonerForever · Answer

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

EgmatQuantExpert · Answer

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

pearljiandani · Answer

I had solved it in the same way, but then I realised that the robots are working on independent dog houses, so we need to calculate how many (complete) dog houses will each of them make in 150 mins. As per your calculation, each robot makes 12.5 houses in an hour, but the last house, the 13th one, isn't complete, and you can't count half the house. So it'll be 12 houses per robot. Hence, 10 robots will make 120 houses in 2.5 hours.

ScottTargetTestPrep · Answer

Solution:
 
Since 2½ hours = 2.5 x 60 = 150 minutes and 150/12 = 12.5, one robot can assemble 12 complete doghouses in 2½ hours. Therefore, 10 robots can assemble 12 x 10 = 120 complete doghouses.

Answer: C

lettercreativensq · Answer

1 machine rate is 1/12
10 m rate will be 10/12 and multiply by 150 min will give 125, how is it 120

plz help

Bunuel · Answer

You should read the question and the discussion more carefully.

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

Your 125 is the total amount of work done, measured in doghouses.

But the question asks for complete doghouses. In 150 minutes, one robot can finish only 12 complete doghouses, because 150/12 = 12.5. The extra 0.5 is just half of another doghouse.

So 10 robots complete:
10 * 12 = 120

The missing 5 comes from 10 half-finished doghouses, not 5 complete ones.

Adit_ · Answer

Is there a way to filter out specific types of questions like these? I remember seeing few more questions where bacteria population grew and then the first time they meet or something like that had the exact same trap. Would be helpful to keep a note of such questions and their wordings to avoid falling into the trap. Thanks!

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards