Step by step
The question
Question: A bus drives 40 km in 50 minutes.
What is its speed in km/h?
1 Find what we know
What do we know?
The bus goes 40 km in 50 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 50 minutes is 50/60, which is 5/6 of an hour.
Careful!
40 divided by 50 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 5x/6 = 40.
Now we solve it.
4 Remove the fraction
The bottom number is 6.
Times 6 will remove it.
We multiply every part by 6.
We do it on both sides, so they stay equal.
6 divided by 6 is 1.
Write what is left.
Do the multiplications.
No more fractions!
5 Remove the 5
5x means 5 times x.
We want just x.
To remove times 5, we divide by 5.
We do it on both sides, so they stay equal.
5 divided by 5 is 1.
So just x is left.
240 divided by 5 is 48.
So x = 48!
6 Answer the question
So the speed is 48 km/h.
7 Check
Let's check in the story.
48 km/h for 5/6 of an hour: 48 times 5/6 is 40 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.