Step by step
The question
Question: A cyclist rides 12 km in 40 minutes.
What is her speed in km/h?
1 Find what we know
What do we know?
The cyclist goes 12 km in 40 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 40 minutes is 40/60, which is 2/3 of an hour.
Careful!
12 divided by 40 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 2x/3 = 12.
Now we solve it.
4 Remove the fraction
The bottom number is 3.
Times 3 will remove it.
We multiply every part by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
Write what is left.
Do the multiplications.
No more fractions!
5 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
36 divided by 2 is 18.
So x = 18!
6 Answer the question
So the speed is 18 km/h.
7 Check
Let's check in the story.
18 km/h for 2/3 of an hour: 18 times 2/3 is 12 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.