Question

If 5 tractors can mow a field in 8 days How many Days would it take to mow the field using 4 tractors. (Use Direct and Inverse variation)

Answer 1

More the tractors, less the days and vice-versa

5/4 = x/8
8*5 = 4*x

x = 10 days

OR
5 tractors can mow a field in 8 days
So, 1 tractor takes 8*5 = 40 days    [tractors inversely prop to days]
Now, 4 tractor takes 40/4 = 10 days
Hope this helps

Answer 2

4 tractors will take 10 days to mow the field if  5 tractors can mow the field in 8 days

Given:

5 tractors can mow a field in 8 days

To Find:

Number of Days taken by 4 tractors to mow the same field

Solution:

Direct Variation: If a variable increases then other variable also increases with a constant factor  i.e.  y = kx

Inverse variation:  if a variable increases then other variable decreases with a  constant factor  i.e   xy = k

As number of tractor increase then number of days decreases as total work is fixed.

Hence this is the case of inverse variation

xy  = k

x = number of tractor

y = number of days

k = work to be done to mow the field

5 tractors can mow a field in 8 days

=> 5(8) = k

=> 40 = k

d days taken by  4 tractors to mow field

4d = k

4d = 40

=> d = 10

Hence 4 tractors will take 10 days to mow the field if  5 tractors can mow the field in 8 days