Step by step
The question
Question: A runner runs 6 km in 30 minutes.
What is his speed in km/h?
1 Find what we know
What do we know?
The runner goes 6 km in 30 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 30 minutes is 30/60, which is 1/2 of an hour.
Careful!
6 divided by 30 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 x/2 = 6.
Now we solve it.
4 Remove the fraction
The bottom number is 2.
Times 2 will remove it.
We multiply every part by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
Write what is left.
Do the multiplications.
No more fractions!
So x = 12!
5 Answer the question
So the speed is 12 km/h.
6 Check
Let's check in the story.
12 km/h for 1/2 of an hour: 12 times 1/2 is 6 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.