## Task 1 - 030821

A rectangular cornfield measuring $360 \mathrm{~m}$ in length and $220 \mathrm{~m}$ in width is to be harvested by two forage harvesters. Samples have shown an average yield of $58 \mathrm{~kg}$ per $10 \mathrm{~m}^{2}$. Each forage harvester can harvest $105 \mathrm{dt}$ per hour.

a) In what time will the cornfield be harvested (assuming continuous operation of both machines)?

b) For the transport of the harvested goods, trailers with a capacity of $3.5 \mathrm{t}$ are available. Each trailer requires a total of 40 minutes for loading, unloading, and the round trip.

How many trailers are needed at a minimum if the work is to proceed continuously?

The answers must be justified!
a) The field has an area of $360 \mathrm{~m} \cdot 220 \mathrm{~m}=79200 \mathrm{~m}^{2}$. The stock thus has a mass of $\frac{58 \mathrm{~kg}}{10 \mathrm{~m}^{2}}$. $79200 \mathrm{~m}^{2}=459360 \mathrm{~kg}=4594 \mathrm{dt}$.

Since both mowers can harvest $210 \mathrm{dt}$ per hour, they will need $\frac{4594}{210}=21.88 \approx 22$ hours.

Each mower harvests $3.5 \mathrm{t}$ in 20 minutes. Assuming that loading and driving to the destination takes as long as unloading and returning, each mower will need two trailers, a total of 4.