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Problem involving productivity and area for planting
Napier Grass has a productivity of about 40 tons of dry mass per hectare per year, which is, for example, at least four times greater than the productivity of eucalyptus wood.
Besides that, it has a 6-month production cycle, while the first cut of eucalyptus wood is done after six years.
Consider a region R, planted with Napier Grass, maintaining constant productivity. If one wants to obtain the same quantity, in tons, of dry mass of eucalyptus, after its first production cycle, it is necessary to plant an area S. What is the relation between S and R?
2. The attempt at a solution
Data:
Productivity of Napier Grass: 40 tons/ha/year
Productivity of eucalyptus wood: 10 tons/ha/year
Napier Grass production cycle: 6 months
Eucalyptus wood production cycle: 6 years
Attempt at a solution:
The quantity of Napier Grass produced in one year in the area R (ha) should be: 40R tons.
(I don't see how the production cycle of Napier Grass is important here, since, in 6 months, the amount produced should simply be 20R tons)
Then, in one eucalyptus production cycle, which is 6 years, the quantity of Napier Grass is: 40R*6 = 240R tons.
In 6 years, the quantity of eucalyptus produced in the area S should be 60S ton (since its productivity is 10 ton per hectare per year).
Since the quantities need to be the same:
60S = 240R
S = 4R
But the correct answer is S = 48R. I don't understand why. I think it has something to do with the different production cycles, but, as I already explained above, I don't see how.
Thank you in advance.
Homework Statement
Napier Grass has a productivity of about 40 tons of dry mass per hectare per year, which is, for example, at least four times greater than the productivity of eucalyptus wood.
Besides that, it has a 6-month production cycle, while the first cut of eucalyptus wood is done after six years.
Consider a region R, planted with Napier Grass, maintaining constant productivity. If one wants to obtain the same quantity, in tons, of dry mass of eucalyptus, after its first production cycle, it is necessary to plant an area S. What is the relation between S and R?
2. The attempt at a solution
Data:
Productivity of Napier Grass: 40 tons/ha/year
Productivity of eucalyptus wood: 10 tons/ha/year
Napier Grass production cycle: 6 months
Eucalyptus wood production cycle: 6 years
Attempt at a solution:
The quantity of Napier Grass produced in one year in the area R (ha) should be: 40R tons.
(I don't see how the production cycle of Napier Grass is important here, since, in 6 months, the amount produced should simply be 20R tons)
Then, in one eucalyptus production cycle, which is 6 years, the quantity of Napier Grass is: 40R*6 = 240R tons.
In 6 years, the quantity of eucalyptus produced in the area S should be 60S ton (since its productivity is 10 ton per hectare per year).
Since the quantities need to be the same:
60S = 240R
S = 4R
But the correct answer is S = 48R. I don't understand why. I think it has something to do with the different production cycles, but, as I already explained above, I don't see how.
Thank you in advance.
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