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In this question, there are several information's already given. Let us first write them down for solving the question.
Amount of money charged by the carpenter for 15 hours = $825
Then
Amount of money charged by the carpenter per hour = 825/15 dollars
                                                                                     = 55 dollars
So the carpenters rate per hour is $55. The cost of the material has no significance with the carpenters rate per hour. The cost of the material has no significance with the carpenter’s rate per hour. The material cost can change as per the customers need. So it cannot be added to the carpenters per hour rate.


Question:- If a carpenter charge $825 for 15hr plus $278 for materials.. What is the carpenters rate per hr

Answer:-

Now, since we need to find the rate per hour, we divide or set up a proportion.

825/15 = x/1

Cross multiply

825*1 = 825
15*x = 15x

15x = 825

Divide

15x/15 = 825/15
x= 825/15
x= 55

Now, since they told us that materials are also in the price, we need to add that too.

$55 per hour + 278 dollars for materials

55+278 = 333

But since the rate means how much, we do not need to include any materials cost. 

We have our final answer:  $55 per hour

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