Step by step
The question
Question: Two trains start 360 km apart and drive toward each other.
One goes 70 km/h and the other goes 50 km/h.
After how many hours do they meet?
1 Find what we know
What do we know?
At the start, they are 360 km apart.
They go toward each other.
One goes 70 km in each hour.
The other goes 50 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.
Train 1: 70 km/h, for x hours.
Train 2: 50 km/h, for x hours.
Distance = speed times time: 70 times x is 70x.
And 50 times x is 50x.
3 Write the equation
In words: the two distances add up to the whole distance.
So the equation is 70x + 50x = 360.
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.
70x + 50x = 120x.
Now we have 120x = 360.
5 Remove the 120
120x means 120 times x.
We want just x.
To remove times 120, we divide by 120.
We do it on both sides, so they stay equal.
120 divided by 120 is 1.
So just x is left.
360 divided by 120 is 3.
So x = 3!
6 Answer the question
So they meet after 3 hours.
7 Check
Let's check in the story.
Train 1: 3 hours at 70 km/h is 210 km.
Train 2: 3 hours at 50 km/h is 150 km.
Together: 360 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.