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Hours of Work (Posted on 2024-05-09)

Two workers were given the job of making a batch of a certain car part. After the first worker had worked for 2h, and the second for 5h, they realised they had only completed half the task. Then after working together for another 3h, they calculated that they still had 5% of the whole task to complete. How long would it take each of them to complete the task, if they worked separately?

No Solution Yet Submitted by Danish Ahmed Khan

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Puzzle Answer

| Comment 1 of 3

Let the first worker complete 1/xth portion and the second worker complete 1/yth portion of the work in 1 hr. when working separately.

Then, we have:

2x+5y =1/2 .....(i)

and, working another 3 hours together, they complete (100-5)= 95% of the task.

So the total amount of work done by them in 3 hrs = (45/100)/3 = 15/100

Then, we have:

x+y = 15/100 ......(ii)

Solving (i) and (ii), we have:

x= 1/12, and: y = 1/15

Consequently, the first worker and the second worker , when working separately, would take the respective times of 12 hrs. and 15 hrs.to complete the task.

Edited on May 9, 2024, 8:46 am

Posted by K Sengupta on 2024-05-09 07:54:16

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