We are given that four gardeners with four mowers can mow 400 square meters in four hours. We are asked to determine how long it will take for eight gardeners with eight mowers to mow 800 square meters. To solve this problem, we first find the mowing rate per gardener and mower combination, then apply it to the new scenario.
Step 1: Calculate the mowing rate of one gardener with one mower. With 4 gardeners and 4 mowers working, they mow 400 square meters in 4 hours. This means:
Rate of 4 gardeners with 4 mowers:
\( \dfrac{400 \text{ sqm}}{4 \text{ hours}} = 100 \text{ sqm/hour} \)
Rate of 1 gardener with 1 mower (divide by 4):
\( \dfrac{100 \text{ sqm/hour}}{4} = 25 \text{ sqm/hour} \)
Step 2: Calculate the time for 8 gardeners with 8 mowers to mow 800 square meters. Now, 8 gardeners with 8 mowers would have a combined rate of:
\( 8 \text{ gardeners} \times 25 \text{ sqm/hour} = 200 \text{ sqm/hour} \)
If they need to mow 800 square meters:
Time required = \( \dfrac{800 \text{ sqm}}{200 \text{ sqm/hour}} = 4 \text{ hours} \)
Therefore, it will take 8 gardeners with 8 mowers 4 hours to mow 800 square meters.