Step by step
The question
Question: A truck takes 5 hours for a trip.
A car takes 4 hours for the same trip.
The car is 15 km/h faster than the truck.
How fast is each one?
1 Find what we know
What do we know?
The truck takes 5 hours.
The car takes 4 hours for the same trip.
The car is 15 km/h faster.
What do we want?
The speed of each one.
2 Name the unknown
We know the car's speed from the truck's speed.
So we call the truck's speed x.
The car is 15 km/h faster: x + 15.
How far each one goes: speed times time.
Let's put it in a table: speed, time, distance.
The truck: x km/h, for 5 hours.
The car: x + 15 km/h, for 4 hours.
Distance = speed times time: 5x.
And 4 times all of x + 15: 4(x + 15).
We keep x + 15 together in brackets.
3 Write the equation
In words: the truck's distance is the same as the car's distance.
So the equation is 5x = 4(x + 15).
Now we solve it.
Careful!
The faster car takes less time: 4 hours.
So 4 goes with x + 15.
Each speed with its own time.
4 Open the brackets
The 4 in front of the bracket multiplies every part inside.
So we write 4 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 4x from the right side.
To remove 4x, we take away 4x.
We do it on both sides, so they stay equal.
4x and − 4x make zero.
Cross them out.
5x − 4x = x.
So x = 60!
6 Answer the question
The car: 60 + 15 = 75.
So the truck goes 60 km/h and the car goes 75 km/h.
7 Check
Let's check in the story.
The truck: 5 hours at 60 km/h is 300 km.
The car: 4 hours at 75 km/h is 300 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.