Step by step
The question
Question: Two cars start 300 km apart and drive toward each other.
One goes 80 km/h and the other goes 70 km/h.
After how many hours do they meet?
1 Find what we know
What do we know?
At the start, they are 300 km apart.
They go toward each other.
One goes 80 km in each hour.
The other goes 70 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: 80 km/h, for x hours.
Car 2: 70 km/h, for x hours.
Distance = speed times time: 80 times x is 80x.
And 70 times x is 70x.
3 Write the equation
In words: the two distances add up to the whole distance.
So the equation is 80x + 70x = 300.
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.
80x + 70x = 150x.
Now we have 150x = 300.
5 Remove the 150
150x means 150 times x.
We want just x.
To remove times 150, we divide by 150.
We do it on both sides, so they stay equal.
150 divided by 150 is 1.
So just x is left.
300 divided by 150 is 2.
So x = 2!
6 Answer the question
So they meet after 2 hours.
7 Check
Let's check in the story.
Car 1: 2 hours at 80 km/h is 160 km.
Car 2: 2 hours at 70 km/h is 140 km.
Together: 300 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.