Step by step
The question
Question: Two cars start 150 km apart and drive toward each other.
One goes 40 km/h and the other goes 20 km/h.
After how many hours do they meet?
1 Find what we know
What do we know?
At the start, they are 150 km apart.
They go toward each other.
One goes 40 km in each hour.
The other goes 20 km in each hour.
What do we want?
When they meet.
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.
Car 1: 40 km/h, for x hours.
Car 2: 20 km/h, for x hours.
Distance = speed times time: 40 times x is 40x.
And 20 times x is 20x.
3 Write the equation
In words: the two distances add up to the whole distance.
So the equation is 40x + 20x = 150.
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.
40x + 20x = 60x.
Now we have 60x = 150.
5 Remove the 60
60x means 60 times x.
We want just x.
To remove times 60, we divide by 60.
We do it on both sides, so they stay equal.
60 divided by 60 is 1.
So just x is left.
We can make 150/60 simpler.
It is the same as 5/2.
So x = 5/2!
6 Answer the question
5/2 is 2.5.
So they meet after 2.5 hours.
7 Check
Let's check in the story.
Car 1: 2.5 hours at 40 km/h is 100 km.
Car 2: 2.5 hours at 20 km/h is 50 km.
Together: 150 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.