SOLUTION: An experienced painter made $600 for working on a certain job. His apprentice, who makes $3 per hour less, also made $600. However, the apprentice worked 10 hours more then the p

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Question 671: An experienced painter made $600 for working on a certain job. His apprentice, who makes $3 per hour less, also made $600. However, the apprentice worked 10 hours more then the painter. How much does the painter make per hour?
Answer by arden42(16) (Show Source):
You can put this solution on YOUR website!
Lets call the painter's hourly rate p, the apprentice's hourly rate a, the painter's hours i and the apprentice's hours h.
This is what we know so far:

Substituting the first and second equations into the 3rd gives:

Since we know ip also equals 600 (according to the 4th equation above), we can say:

Expand the brackets:

Since we want to find p, we need to express i in terms of p. To do this, we make i the subject:

Now, if we substitute this value for i into the 4th of our original equations:

Expand the brackets:

Remove fractions and get everything on one side:

Divide everything by 10:

Now we have a quadratic we can factorise:

So p equals either 15 or -12. Since the painter can't be charging a negative rate, he must earn $15 an hour.