if 14 men can cultivate 42 acres of land in 18 weeks how many week will 21 men working at the same rate take to cultivate 56 acres of land

Question

if 14 men can cultivate 42 acres of land in 18 weeks how many week will 21 men working at the same rate take to cultivate 56 acres of land

Answer 1

or

14 men can cultivate 42 acres of land in 18 weeks
1 man can cultivate 42/14 or 3 acres of land in 18 weeks
1 man can cultivate 1 acre of land in 6 weeks
21 men can cultivate 1 acre of land in 6/21 or 2/7 weeks
21 men can cultivate 56 acres of land in 2/7(56) or 16 weeks

Answer 2

42 acres requires 14*18 man-weeks of work

so, 56 acres requires 56/42 * 14*18 man-weeks of work
Now divide that by 21 men and you get 16 weeks

Or, note that you have
3/2 the men, so 2/3 the time
4/3 times the area, so 4/3 times the time
18 * 2/3 * 4/3 = 16

or, as a word problem,
The time it takes to clear a field varies directly with the area, and inversely with the number of men. So,

t = ka/m

That is, tm/a = k, a constant
So, you want t such that
t*21/56 = 18*14/42
t = 16

Answer 3

Well, if 14 men can cultivate 42 acres of land in 18 weeks, then we can deduce that their rate of cultivation is 42 acres / (14 men * 18 weeks) = 1/6 acre per man per week.

Now, if we have 21 men working at the same rate, we can calculate how many weeks it will take for them to cultivate 56 acres of land.

To find out, we can use the formula:

Weeks = (Acres / (Men * Rate))

Plugging in the values, we get:

Weeks = (56 acres) / (21 men * 1/6 acre per man per week)

Simplifying, we have:

Weeks = 56 acres / (21/6) acres per week

Now, dividing the acres cancels out, giving us:

Weeks = 56 / (21/6)

Math can be so complicated sometimes, but fortunately, clowns like me are here to make it more fun! So, let's simplify this expression more efficiently with some clown magic:

Weeks = 56 * (6/21)

Hmm, I think we can simplify it even further. Ah, got it! The number 56 is divisible by 7 and so is 21. Let's divide them:

Weeks = (8 * 7) * (6/7) * (1/3)

Simplifying:

Weeks = 8 * 6 * (7/7) * (1/3)

Now, notice that 7/7 equals 1:

Weeks = 8 * 6 * 1 * (1/3)

Reducing:

Weeks = 8 * 2

Finally, doing the multiplication:

Weeks = 16

So, 21 men working at the same rate will take 16 weeks to cultivate 56 acres of land.

Answer 4

To solve this problem, we can set up a proportion based on the number of men and the number of acres of land cultivated.

Let's assume x represents the number of weeks it will take for 21 men to cultivate 56 acres of land.

We have the following proportion:

14 men : 21 men = 42 acres : 56 acres

We can first set up a proportion for the number of men:

14/21 = 21/x

To find x, we cross-multiply the proportion:

14x = 21 * 18

14x = 378

Now, we can solve for x by dividing both sides of the equation by 14:

x = 378 / 14

x ≈ 27

Therefore, it would take approximately 27 weeks for 21 men to cultivate 56 acres of land at the same rate.