If 14 men cultivates 42 acres of land in 18 weeks, how many weeks will 21 men working at the same rate take to cultivate 56 acres of land.?
acres = k(men * time)
given: acres = 42, time = 18, men=14
42 = k(14)(18)
k = 1/6
acres = (1/6)(men)(time)
56 = (1/6)(21)(time)
time = 6*56/21 = 16
or:
14 men cultivate 42 acres of land in 18 weeks
1 man cultivates 42/14 acres of land in 18 weeks
21 men cultivate 42/14*21 acres of land in 18 weeks
21 men cultivate 63 acres of land in 18 weeks
21 men cultivate 1 acre of land in 18/63 week
21 men cultivate 56 acres of land in 18/63*56 weeks
21 men cultivate 56 acres of land in 16 weeks
I didn't understand this formula pls explain the procedure, thanks.
To find out how many weeks it will take for 21 men to cultivate 56 acres of land, we can use proportions.
First, let's set up a proportion to determine the relationship between the number of men and the number of acres they can cultivate in a given time period.
14 men can cultivate 42 acres in 18 weeks.
So, we can write the proportion as:
14 men / 42 acres = 21 men / 56 acres
Now, cross-multiply:
14 men * 56 acres = 42 acres * 21 men
784 man-acres = 882 man-acres
Next, divide both sides of the equation by 882 to solve for the number of weeks it will take the 21 men to cultivate 56 acres:
784 man-acres / 882 man-acres = 56 acres / x weeks
Simplifying, we have:
0.8889 = 56 / x
Cross-multiply and divide to solve for x:
0.8889x = 56
x = 56 / 0.8889
x ≈ 62.98
Therefore, it will take approximately 62.98 weeks for 21 men to cultivate 56 acres of land at the same rate.
To solve this problem, we can set up a proportion based on the given information.
First, let's find out how much land can be cultivated by one man in one week. We can do this by dividing the total land cultivated by the total number of men and the total number of weeks:
Land cultivated by one man in one week = 42 acres / (14 men × 18 weeks)
= 42 acres / (252 man-weeks)
Now we can find out how many weeks it would take for 21 men to cultivate 56 acres of land. Let's set up a new proportion using the previous result:
Weeks needed for 21 men to cultivate 56 acres = (56 acres) / ((21 men) × Land cultivated by one man in one week)
Substituting the value we calculated earlier:
Weeks needed for 21 men to cultivate 56 acres = (56 acres) / ((21 men) × (42 acres / 252 man-weeks))
Simplifying further:
Weeks needed for 21 men to cultivate 56 acres = (56 / 21) × (252 / 42)
We can cancel out common factors to simplify this fraction:
Weeks needed for 21 men to cultivate 56 acres = (8 / 3) × (6 / 1)
Multiplying these values:
Weeks needed for 21 men to cultivate 56 acres = (8 × 6) / (3 × 1)
= 48 / 3
= 16 weeks
Therefore, it would take 21 men working at the same rate 16 weeks to cultivate 56 acres of land.