A farmer can plow a given field in 7 hours. If his son helps him, they can plow the field together in 4 hours. How long would it take his son to plow the field alone? Express your answer as a fraction reduced to lowest terms, if needed.

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Well, let's do some math in the most amusing way possible! If it takes the farmer 7 hours to plow the field alone, we can imagine him plowing away with his big plow like a tractor. Now, when his son joins in, they become like a plow tag team, working together to finish the job faster. In fact, they complete the task in just 4 hours!

So, let's figure out how much work the son does in 1 hour. Since the farmer and his son working together can plow the field in 4 hours, that means they do 1/4 of the field in 1 hour. Now, if the son was to plow the field alone, he would take t hours to finish it. This means that the son completes 1/t of the field in 1 hour.

If we add up these two fractions of work: 1/4 for both of them working together and 1/t just for the son, it should equal the whole field. That gives us the equation 1/4 + 1/t = 1. But you know what? It's a bit easier to understand if we get rid of those pesky fractions.

If we multiply the equation by 4t, we get t + 4 = 4t. Solving this equation, we find t = 4/3.

So, the son would take 4/3 hours to plow the field alone. And that, my friend, is the fraction reduced to its lowest terms. Happy plowing!

To solve this problem, we can use the concept of work.

Let's denote the farmer's rate of work as X (in terms of how much of the field he can plow per hour). Therefore, in 7 hours, he can plow 7X of the field.

We can denote the son's rate of work as Y. So in 4 hours, the farmer and his son working together can plow 4(X + Y) of the field.

From the given information, we know that when they work together, they can plow the entire field. Therefore, we can set up the following equation based on the work done:

7X = 4(X + Y)

Now we can solve this equation to find the value of Y, which represents the son's rate of work.

Expanding the equation, we get:

7X = 4X + 4Y

Next, we can simplify the equation by combining like terms:

3X = 4Y

Now, divide both sides of the equation by 4:

(3X)/4 = Y

So, the son's rate of work is (3X)/4.

To find how long it would take the son to plow the field alone, we need to find the reciprocal of the son's rate of work. Therefore, the son would take 4/(3X) hours to plow the field alone.

Please note that we cannot determine the exact time in hours without knowing the value of X (the farmer's rate of work) or more specific information.

If the son takes x hours,

1/7 + 1/x = 1/4

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