Step by step
The question
Question: A truck leaves a city at 60 km/h.
1 hour later, a car leaves the same city on the same road at 80 km/h.
How many hours does the car take to catch up?
1 Find what we know
What do we know?
The truck goes 60 km in each hour.
The car leaves 1 hour later.
The car is faster: 80 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 truck left 1 hour before.
So it drives 1 more: x + 1.
How far each one goes: speed times time.
Let's put it in a table: speed, time, distance.
The truck: 60 km/h, for x + 1 hours.
The car: 80 km/h, for x hours.
Distance = speed times time: 60(x + 1).
We keep x + 1 together in brackets.
And 80 times x: 80x.
3 Write the equation
In words: the car's distance is the same as the truck's distance.
So the equation is 80x = 60(x + 1).
Now we solve it.
4 Open the brackets
The 60 in front of the bracket multiplies every part inside.
So we write 60 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 60x from the right side.
To remove 60x, we take away 60x.
We do it on both sides, so they stay equal.
60x and − 60x make zero.
Cross them out.
80x − 60x = 20x.
Now we have 20x = 60.
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.
60 divided by 20 is 3.
So x = 3!
7 Answer the question
So the car catches up after 3 hours.
8 Check
Let's check in the story.
The car: 3 hours at 80 km/h is 240 km.
The truck drove 1 hours more: 4 hours at 60 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.