Owen harvested 2400 hectares of canola in 12 days using 4 machines. How long would it take to harvest 3600 hectares if he used 6 machines?
2400 hectares of canola in 12 days using 4 machines
600 hectares of canola in 12 days using 1 machine
3600 hectares of canola in 12 days using 6 machines
or
time is directly proportional with the acreage and inversely with the number of machines
T = k (A/M)
given:
12 = k(2400/4)
12 = 600k
k = 12/600 = 1/50
T = A/(50M)
so when A = 3600, and M = 6
T = 3600(50(6)) = 12
To find out how long it would take to harvest 3600 hectares with 6 machines, we can set up a proportion.
Let's denote the time it takes to harvest 3600 hectares with 6 machines as "t" days.
The proportion can be set up as follows:
2400 hectares / 12 days = 3600 hectares / t days
To solve for "t," we can cross-multiply:
2400 hectares * t days = 3600 hectares * 12 days
2400t = 43,200
Divide both sides of the equation by 2400:
t = 43,200 / 2400
t = 18
Therefore, it would take 18 days to harvest 3600 hectares if Owen used 6 machines.
To find out how long it would take to harvest 3600 hectares with 6 machines, we can use a proportional relationship between the number of hectares and the number of days.
We have the following information:
- Owen harvested 2400 hectares in 12 days using 4 machines.
- The number of hectares is directly proportional to the number of days.
First, we need to determine the harvesting rate for 1 machine:
2400 hectares / 12 days = 200 hectares per day.
Next, we can determine the new harvesting rate with 6 machines:
200 hectares per day * 6 machines = 1200 hectares per day.
Finally, we can find the number of days it would take to harvest 3600 hectares with the new harvesting rate:
3600 hectares / 1200 hectares per day = 3 days.
Therefore, it would take 3 days to harvest 3600 hectares if Owen used 6 machines.