Step by step
The question
Question: A train travels 90 km in 45 minutes.
What is its speed in km/h?
1 Find what we know
What do we know?
The train goes 90 km in 45 minutes.
What do we want?
The speed, in km per hour.
2 Name the unknown
We don't know the speed.
So we call it x km/h.
Speed is in km per hour.
So the time must be in hours too.
1 hour is 60 minutes.
So 45 minutes is 45/60, which is 3/4 of an hour.
Careful!
90 divided by 45 gives km in each minute, not in each hour.
So we use the time in hours.
How far we go: speed times time.
3 Write the equation
In words: speed times time makes the distance.
So the equation is 3x/4 = 90.
Now we solve it.
4 Remove the fraction
The bottom number is 4.
Times 4 will remove it.
We multiply every part by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
Write what is left.
Do the multiplications.
No more fractions!
5 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
360 divided by 3 is 120.
So x = 120!
6 Answer the question
So the speed is 120 km/h.
7 Check
Let's check in the story.
120 km/h for 3/4 of an hour: 120 times 3/4 is 90 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.