Step by step
The question
Question: Ravi can tile a floor in 10 hours.
Dev can tile it in 40 hours.
How many hours will it take them to tile it together?
1 Find what we know
What do we know?
Ravi does the whole job alone in 10 hours.
Dev does it alone in 40 hours.
What do we want?
How long it takes them together.
2 Name the unknown
We don't know how long it takes together.
So we call it x hours.
Careful!
Many people add the times: 50 hours.
But two working together are faster than one.
So together it takes less than 10 hours.
The whole floor is 1 whole job.
We split it into parts.
Let's put it in a table: the time alone, and the part done.
Ravi does the whole job in 10 hours.
So in 1 hour, Ravi does 1 part out of 10.
That is 1/10.
Dev does 1 part out of 40 in 1 hour: 1/40.
In x hours, Ravi does x times as much: x/10.
And Dev does x/40.
3 Write the equation
In words: Ravi's part plus Dev's part makes the whole job.
So the equation is x/10 + x/40 = 1.
Now we solve it.
4 Remove the fractions
The bottom numbers are 10 and 40.
40 can be divided by all of them.
We multiply every part by 40.
We do it on both sides, so they stay equal.
40 divided by 10 is 4.
40 divided by 40 is 1.
Write what is left.
Do the multiplications.
No more fractions!
5 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
4x + x = 5x.
Now we have 5x = 40.
6 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.
40 divided by 5 is 8.
So x = 8!
7 Answer the question
So together it takes 8 hours.
8 Check
Let's check in the story.
In 8 hours, Ravi does 8/10.
That is 4/5 of the floor.
In 8 hours, Dev does 8/40.
That is 1/5 of the floor.
Together: 4/5 plus 1/5 is 5/5.
That is 1 whole floor, like the story says.
Does it make sense?
Together is faster than Ravi alone, who needs 10 hours.
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.