Step by step
The question
Question: Two friends leave the same place and walk in opposite directions.
One walks at 4 km/h and the other at 5 km/h.
After how many hours are they 18 km apart?
1 Find what we know
What do we know?
They start at the same place.
They go opposite ways.
One goes 4 km in each hour.
The other goes 5 km in each hour.
We want them 18 km apart.
What do we want?
When they are 18 km apart.
2 Name the unknown
We don't know how many hours.
So we call it x.
Both go for the same x hours.
How far each one goes: speed times time.
Let's put it in a table: speed, time, distance.
Friend 1: 4 km/h, for x hours.
Friend 2: 5 km/h, for x hours.
Distance = speed times time: 4 times x is 4x.
And 5 times x is 5x.
3 Write the equation
In words: the two distances add up to the whole distance.
So the equation is 4x + 5x = 18.
Now we solve it.
4 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
4x + 5x = 9x.
Now we have 9x = 18.
5 Remove the 9
9x means 9 times x.
We want just x.
To remove times 9, we divide by 9.
We do it on both sides, so they stay equal.
9 divided by 9 is 1.
So just x is left.
18 divided by 9 is 2.
So x = 2!
6 Answer the question
So after 2 hours they are 18 km apart.
7 Check
Let's check in the story.
Friend 1: 2 hours at 4 km/h is 8 km.
Friend 2: 2 hours at 5 km/h is 10 km.
Together: 18 km, like the story says.
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.