It takes 7 gardeners 8 hours to plant 1680 seedlings on a piece of land.
Calculate (in hours and minutes) how long it would take 12 gardeners to
plant the same seedlings.

Question

It takes 7 gardeners 8 hours to plant 1680 seedlings on a piece of land. Calculate (in hours and minutes) how long it would take 12 gardeners to plant the same seedlings.

UpStudy AI · Accepted Answer

1. Determine the total work in gardener-hours needed to plant the seedlings.  
   Since 7 gardeners take 8 hours to plant 1680 seedlings, the total work is  
   $$
   7 \times 8 = 56 \text{ gardener-hours}
   $$

2. Calculate the number of seedlings planted per gardener-hour.  
   $$
   \text{Seedlings per gardener-hour} = \frac{1680}{56} = 30
   $$
   This means one gardener plants 30 seedlings in one hour.

3. For 12 gardeners, calculate the combined rate per hour.  
   $$
   \text{Combined rate} = 12 \times 30 = 360 \text{ seedlings per hour}
   $$

4. Determine the time required for 12 gardeners to plant 1680 seedlings.  
   $$
   \text{Time (in hours)} = \frac{1680}{360} = \frac{14}{3} \approx 4.6667 \text{ hours}
   $$

5. Convert the decimal hours to hours and minutes.  
   The fractional part $$0.6667$$ hours is  
   $$
   0.6667 \times 60 \approx 40 \text{ minutes}
   $$

6. Final Answer:  
   $$4$$ hours and $$40$$ minutes.
It would take 12 gardeners 4 hours and 40 minutes to plant the same number of seedlings.

It takes 7 gardeners 8 hours to plant 1680 seedlings on a piece of land.
Calculate (in hours and minutes) how long it would take 12 gardeners to
plant the same seedlings.

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