Twelve farmers can harvest 2 hectares of rice in 3 days. How many farmers will it take to harvest 5 hectares in 10 days?
12 farmers * 3 days = 2 hectares
multiply by 5/2 and you have
12(5/2) farmers * 3 days = 5 hectares
Now on the left, multiply by (3/10)(10/3):
12(5/2)(3/10) farmers * 3(10/3) days = 5 hectares
9 farmers * 10 days = 5 hectares
or
12f * 3d = 2h
9f * 4d = 2h
9f * 10d = 2(5/2) = 5h
Well, it sounds like these farmers are pretty efficient with their rice harvesting! Let's do some calculations here. If twelve farmers can harvest 2 hectares of rice in 3 days, that means they can harvest 2/12 or 1/6 of a hectare per day.
Now, let's figure out how many hectares they can harvest in 10 days. Since they can harvest 1/6 of a hectare per day, in 10 days they can harvest 10*(1/6) = 5/3 hectares of rice.
Therefore, if you want to harvest 5 hectares in 10 days, you would need more than twelve farmers, because they can only harvest 5/3 hectares in that time. However, since we can't have fractional farmers, I guess you could have thirteen farmers and hope that one of them brings a magic wand to make up the extra hectares!
To solve this problem, let's first calculate the rate at which the twelve farmers can harvest rice.
Rate = Area / Time
Rate = 2 hectares / 3 days
Rate = 2/3 hectares per day
Next, let's determine how many farmers are needed to harvest 5 hectares in 10 days.
Rate = Area / Time
Rate = 5 hectares / 10 days
Since the rate at which the twelve farmers can harvest rice is 2/3 hectares per day, we can set up a proportion:
(2/3) hectares per day / 12 farmers = (5 hectares / 10 days) / X farmers
Cross-multiplying:
(2/3) hectares per day * X farmers = (5 hectares / 10 days) * 12 farmers
Simplifying:
(2/3) * X = (5/10) * 12
(2/3) * X = 6
Multiplying both sides by (3/2):
X = 6 * (3/2)
X = 18/2
X = 9
Therefore, it would take 9 farmers to harvest 5 hectares in 10 days.
To solve this problem, we can use the concept of "worker-hours" or "man-hours." This represents the total amount of work done by a worker in one hour.
Let's first calculate the worker-hours needed to harvest 2 hectares of rice in 3 days. Since there are 12 farmers working, each working for 3 days, the total worker-hours can be calculated as follows:
Worker-hours for 2 hectares = 12 farmers × 3 days × 24 hours/day = 864 worker-hours
Next, we need to determine the worker-hours needed per hectare. Since 2 hectares require 864 worker-hours, we can find the worker-hours needed per hectare as:
Worker-hours per hectare = 864 worker-hours / 2 hectares = 432 worker-hours/hectare
Now, let's calculate the number of farmers needed to harvest 5 hectares in 10 days. Assuming the worker-hours per hectare remains the same, we can calculate the total worker-hours required for 5 hectares as:
Total worker-hours for 5 hectares = Worker-hours per hectare × 5 hectares = 432 worker-hours/hectare × 5 hectares = 2160 worker-hours
Since we want to find the number of farmers, we need to divide the total worker-hours by the number of worker-hours a single farmer can contribute in 10 days:
Number of farmers = Total worker-hours / (10 days × 24 hours/day)
Number of farmers = 2160 worker-hours / (10 days × 24 hours/day) = 9 farmers
Therefore, it would take 9 farmers to harvest 5 hectares in 10 days.