A local charity is wrapping holiday gifts for local needy families. When 8 volunteers work together, they can get all the gifts wrapped and distributed in 6 hours. How many hours would it have taken if there had been 12 volunteers, each working at the same rate?

If n workers do a job in h hours, that means n × h = the job
If m workers do the same job in t hours, that means m × t = the job
Then n × h = m × t, if n > m then h < t and vice versa, if n < m then h > t, this relation is called inverse proportion

A local charity is wrapping holiday gifts for local needy families. When 8 volunteers work together, they can get all the gifts wrapped and distributed in 6 hours.

We need to find how many hours would it have taken if there had been 12 volunteers, each working at the same rate

Let us used the rule above

∵ 8 volunteers can get all the gifts wrapped and distributed in 6 hours

∵ 12 volunteers can do that with the same rate

- The number of volunteers increased, then the number of hours

must be decreased

∴ 8 × 6 = 12 × t, where t is the number of hours

∴ 48 = 12 t

- Divide both sides by 12

∴ 4 = t

∴ The 12 volunteers can get all the gifts wrapped and distributed

in 12 hours

It would have taken 4 hours if there had been 12 volunteers, each working at the same rate

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You can learn more about inverse variation in brainly.com/question/10708697

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