perplexus.info :: Just Math : Hours of Work

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?

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| Comment 2 of 3 |

After working together for three hours they finished 45%=9/20 of the job. So working together they can do (9/20)/3=3/20 jobs/hour.

During the two hours leading up to the half-way point the two guys did 2*(3/20)=3/10 jobs.

During the three hours Second Guy was working alone he did 1/2-3/10=1/5 jobs. So then he works at a rate of (1/5)/3=1/15 jobs/hour.

That leaves First Guy working at a rate of 3/20-1/15=1/12 jobs/hour.

Then First Guy working alone would take 12 hours to finish the job alone and the Second Guy working alone would take 15 hours to finish the job.

Posted by Brian Smith on 2024-05-09 10:14:44

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