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# Word Problems/Unit Rate Calculation

Question
QUESTION: Hello:

6 workers can finish a job in 10 hours, 12 workers can finish the same job in how many hours?

Can you use the following to determine the answer?  I provided a calculation, but I do not know that it is correct.

1 worker does 1/6 of the job in 10 hours.
1/6 job/(10 hours) = 1/6 divided by 10 job/hour = 1/60 job/hour
1 worker does 1/60 of the job per hour.

Would 12 workers be divided by 1/60 of the job per hour?

12 workers divided by 1/60 job/hour. (?)

The calculation needs "worker" as in 12 workers divided by 1/60 job/hour per worker so that "worker" cancels from the calculation.

ANSWER: You have determined that each worker can do 1/60 of a job in an hour.

Multiplying this by 12 workers give 1/5 of a job per hour.

The means to complete the whole job take 5 hours, so 5 * 1/5 = 1 job.

---------- FOLLOW-UP ----------

QUESTION: Hello:

I want to thank you for the reply.

How do the "worker" units cancel from the calculation  or do they not cancel?

If a worker makes \$7 / hour, and you have 4 workers, the price is really 7\$ / (hour * worker).
That way when the \$7 is multiplied by the number of workers, the hourly wage for all the workers of the same type is found.

Since the units calculated here are in dollars / hour, when multiplying by the number of hours, a dollar value is gotten.

Units in problems are important and it is valuable to put them in the right spot.

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks for the reply!

Word Problems

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#### Scott A Wilson

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