Step by step
The question
Question: Mia can mow a lawn in 4 hours.
Working together, Mia and Leo can mow it in 2 hours.
How long would it take Leo alone?
1 Find what we know
What do we know?
Mia does the whole job alone in 4 hours.
Together they take 2 hours.
What do we want?
How long Leo takes alone.
2 Name the unknown
We don't know how long Leo takes alone.
So we call it x hours.
Careful!
Many people take away the times: 2 hours.
But Leo alone is slower than the two together.
So it takes more than 2 hours.
The whole lawn is 1 whole job.
We split it into parts.
Let's put it in a table: the time alone, and the part done.
Mia does the whole job in 4 hours.
So in 1 hour, Mia does 1 part out of 4.
That is 1/4.
Leo takes x hours alone.
So in 1 hour, Leo does 1 over x.
They work 2 hours together.
In 2 hours, Mia does 2 times as much: 2/4.
And Leo does 2 over x.
3 Write the equation
In words: Mia's part plus Leo's part makes the whole job.
So the equation is 2/4 + 2/x = 1.
Now we solve it.
First: a bottom can never be 0.
x at the bottom can't be 0.
So x ≠ 0.
4 Remove the fractions
The bottoms are 4 and x.
4x can be divided by all of them.
We multiply every part by 4x.
We do it on both sides, so they stay equal.
4x divided by 4 is x.
4x divided by x is 4.
4x times 1 is 4x.
Write what is left.
No more fractions!
5 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 2x from the left side.
To remove 2x, we take away 2x.
We do it on both sides, so they stay equal.
2x and − 2x make zero.
Cross them out.
4x − 2x = 2x.
Now we have 8 = 2x.
Let's swap the two sides, so x is on the left.
6 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
8 divided by 2 is 4.
So x = 4!
7 Answer the question
So Leo alone takes 4 hours.
8 Check
Let's check in the story.
In 2 hours, Mia does 2/4, and Leo does 2/4.
2/4 plus 2/4 is 4/4.
That is 1 whole lawn, like the story says.
Does it make sense?
Leo alone is slower than the two together.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.