contestada

The time required for a crew of men to do a job is inversely proportional to the product
of the number of men and the number of hours they work per day. If a crew of 15 men
working 5 hrs a day do a job in 10 days, find how long it would take 10 men working 6
hours a day to do the job.

Respuesta :

Using proportionality, it is found that it would take them 12.5 days.

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  • The measures are: time t, number of men m and number of hours h.
  • The time is inversely proportional to the product of the number of men and of the number of hours, thus, the equation that relates these measures is:

[tex]t = \frac{k}{mh}[/tex]

  • In which k is the constant of proportionality.

  • 15 men working 5 hours a day take 10 days, thus [tex]m = 15, h = 5, t = 10[/tex], and we use it to find k.

[tex]t = \frac{k}{mh}[/tex]

[tex]10 = \frac{k}{15(5)}[/tex]

[tex]k = 15 \times 5 \times 10 = 750[/tex]

Thus

[tex]t = \frac{750}{mh}[/tex]

  • The time with 10 men and 6 hours is:

[tex]t = \frac{750}{mh} = \frac{750}{10(6)} = \frac{750}{60} = 12.5[/tex]

It would take them 12.5 days.

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