Algebra Question?

Question

A farmer can plow a field in 4 days by using a tractor. A hired hand can plow the same field in 6 days by using a smaller tractor. How many days will be required for the plowing of this field if they work together?

I got that it was one and a half days and just wanted to confirm it.

Answer 1

Let

1/4 the larger Tractor time

1/6 the smaller tractor time

1 equals the two tractors together

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1/4x + 1/6x = 1

The common denominator is 12

12(1/4x) + 12(1/6x) = 12(1)

3x + 2x = 12

5x = 12

5x/5 = 12/5

x = 2.4

The answer is x = 2.4

The solution set is { 2.4 }

Insert the x value into the equation

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Chedk

1/4x + 1/6x = 1

1/4(2.4) + 1/6(2.4) = 1

2.4/4 + 2.4/6 = 1

0.6 + 0.4 = 1

1 = 1

Answer 2

I get 5 Days.
I added 4 plow days to 6 plow days and divided by 2 People Plowers. We should be able to cancel out the 10 Plows and the 2 People Plowers and be left with only 5 Days.

Answer 3

5 days

Answer 4

well heres what i got and how i did it. I got a different answer but im not sure if mine is right so dont hold me to my answer.


(1/4)x + (1/6)x = 1

(6/24)x + (4/24)x = 1

(10/24)x = 1

x = (24/10) or x = 2.4 days


do not listen to george he is just giving you the average between the 2, not the time it takes working together.

Answer 5

I got the same answer as the guy above but I did it a little different.
x = work done by farmer
y = work done by tractor
z = days when they work together
A = Area of the field


4x = A
6y = A
4x = 6y
x = (3/2)y
A = z(y + x)
6y = z(y+(3/2y))
6 = (5/2)z
z = 12/5 = 2.4

Answer 6

3.5 days

Answer 7

2.25 days.