Step by step
The question
Question: A bus takes 4 hours for a trip.
A car takes 3 hours for the same trip.
The car is 20 km/h faster than the bus.
How fast is each one?
1 Find what we know
What do we know?
The bus takes 4 hours.
The car takes 3 hours for the same trip.
The car is 20 km/h faster.
What do we want?
The speed of each one.
2 Name the unknown
We know the car's speed from the bus's speed.
So we call the bus's speed x.
The car is 20 km/h faster: x + 20.
How far each one goes: speed times time.
Let's put it in a table: speed, time, distance.
The bus: x km/h, for 4 hours.
The car: x + 20 km/h, for 3 hours.
Distance = speed times time: 4x.
And 3 times all of x + 20: 3(x + 20).
We keep x + 20 together in brackets.
3 Write the equation
In words: the bus's distance is the same as the car's distance.
So the equation is 4x = 3(x + 20).
Now we solve it.
Careful!
The faster car takes less time: 3 hours.
So 3 goes with x + 20.
Each speed with its own time.
4 Open the brackets
The 3 in front of the bracket multiplies every part inside.
So we write 3 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 3x from the right side.
To remove 3x, we take away 3x.
We do it on both sides, so they stay equal.
3x and − 3x make zero.
Cross them out.
4x − 3x = x.
So x = 60!
6 Answer the question
The car: 60 + 20 = 80.
So the bus goes 60 km/h and the car goes 80 km/h.
7 Check
Let's check in the story.
The bus: 4 hours at 60 km/h is 240 km.
The car: 3 hours at 80 km/h is 240 km.
The same trip, like the story says.
Does it make sense?
The car is faster, and it takes less time.
That makes sense.
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.