Step by step
The question
Question: A bus leaves a town at 40 km/h.
2 hours later, a car leaves the same town on the same road at 60 km/h.
How many hours does the car take to catch up?
1 Find what we know
What do we know?
The bus goes 40 km in each hour.
The car leaves 2 hours later.
The car is faster: 60 km in each hour.
What do we want?
How many hours the car drives until it catches up.
2 Name the unknown
We don't know how long the car drives.
So we call it x hours.
The bus left 2 hours before.
So it drives 2 more: x + 2.
How far each one goes: speed times time.
Let's put it in a table: speed, time, distance.
The bus: 40 km/h, for x + 2 hours.
The car: 60 km/h, for x hours.
Distance = speed times time: 40(x + 2).
We keep x + 2 together in brackets.
And 60 times x: 60x.
3 Write the equation
In words: the car's distance is the same as the bus's distance.
So the equation is 60x = 40(x + 2).
Now we solve it.
4 Open the brackets
The 40 in front of the bracket multiplies every part inside.
So we write 40 times each part.
Work out each multiplication.
5 Get x on one side
There is x on both sides.
We want x on one side only.
So we remove the 40x from the right side.
To remove 40x, we take away 40x.
We do it on both sides, so they stay equal.
40x and − 40x make zero.
Cross them out.
60x − 40x = 20x.
Now we have 20x = 80.
6 Remove the 20
20x means 20 times x.
We want just x.
To remove times 20, we divide by 20.
We do it on both sides, so they stay equal.
20 divided by 20 is 1.
So just x is left.
80 divided by 20 is 4.
So x = 4!
7 Answer the question
So the car catches up after 4 hours.
8 Check
Let's check in the story.
The car: 4 hours at 60 km/h is 240 km.
The bus drove 2 hours more: 6 hours at 40 km/h is 240 km.
The same distance: the car has caught up.
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.