Need mathematician again....?

Question

A farmer can plow a certain field three times as fast as his son. Working together, it will take them 6 hours to plow the field. How long will it take each to do it alone. (will you tell me how to solve it step by step.. so that i will learn... pls..)

Answer 1

The trick to doing questions like this is to "invert" the info. Instead of saying "John can mow a lawn/paint a wall/satisfy his wife in 2 hours," we say "John can mow 1/2 his lawn/paint 1/2 his wall/satisfy 1/2 his wife in one hour."

So: In one hour, let's say the son can plow x fields in one hour. (x will wind up being some fraction, like 1/10 of a field.) The farmer can plow 3x fields in that same hour. Together, they can plow 1/6 of a field. The equation:

x + 3x = 1/6.

We combine the terms on the left:

4x = 1/6

And now we divide both sides by 4:

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

So the son can plow 1/24 of the field in one hour, or 1 field in 24 hours. The farmer can plow three times as much: 3/24 = 1/8 of the field in one hour, or 1 field in 8 hours.

Hope that makes sense. Good luck with your studies!

Answer 2

Hmm, we just did this problem in algebra class this morning.

Here's what I would do:

farmer + son = 6 hours
farmer = 3x son

Now let's put that in math format:
x + y = 6
x = 3y

Now you have a value for x; it's either 6 - y or 3y. Can you see how I got that?

x = 3y
x = 6 - y

Now look at the first equation; you can solve it for y by replacing "x" with one of the values for "y" above:

3y + y = 6
4y = 6
y = 6/4
y = 1 1/2

Look again at the first equation, and replace y with the value we've just determined, so we can determine the real value of x:

x + 1 1/2 = 6
x = 6 - 1 1/2
x = 4 1/2

To prove your answers, place the values into the second equation and see if that equation has been solved:

x = 3y
4 1/2 = 3(1 1/2)
4 1/2 = 4 1/2

Yes, those values (1 1/2, 4 1/2) are the unique solution to your word problem!

Answer 3

A farmer ok let him be (a)
His son (3a) because he can plow a field 3 times his father's time
so together they get the job done in 6 hours
So
(3a)+(a)=6 same variable can be added together
4a=6 you need to get the variable by its self
4/4 a=6/4
a=6/4 an improper fraction can be readused to
a=1.5 or as a fraction a=1 1/2 which his fathers time
the sons time is (3a) so you plug in (a) to get his time
so 3*1.5 = 4.5 which is the sons time

Answer 4

Turn it all into multiples of the smallest amount of action - the son does the least in a given amount of time , the farmer is as good as three sons. so 4 sons take 6 hours.

now you can easily work out how long 1 son will take ( not counting breaks for meals and sleeping) . Plus you know that the farmer takes only 1/3rd the time his son would take.

Best of Luck - Mike

Answer 5

Farmer = F
Son = S

F = 3S

F + S = 6

3S + S = 6

4S = 6

Son takes 3/2 hours

F = 3S
F = 3(3/2)

Father takes 9/2 hours


wait a sec its the other way around

Answer 6

Let f = rate for the farmer
s = rate for the son
f=2s from the first statement
Working together they will plow at a rate of s+2s=3s
A/(3s)=6
A/s = 18 hr
A/f = 18/2 = 9 hr