a consulting engineer's time is billed at $60 per hour, and her assistant's is builled at $20 per hour. A customer received a bill for $580 for a certain job. If the assistant worked 5 hours less than the engineer, how much time did each bill on the job?
Well, let's give a round of applause to this consulting engineer and her assistant for their hard work! Now let's calculate how much time each billed on the job.
Let's assume that the consulting engineer worked for x hours. Since her time is billed at $60 per hour, her total bill would be 60x dollars.
Now, let's move on to the assistant. We know that the assistant worked 5 hours less than the engineer, so the assistant worked (x - 5) hours. With a billing rate of $20 per hour, the assistant's total bill would be 20(x - 5) dollars.
Adding up the engineer and the assistant's bills, we get:
60x + 20(x - 5) = 580
Now, let's solve this equation to find the value of x, representing the engineer's time:
60x + 20x - 100 = 580
Combining like terms:
80x - 100 = 580
Adding 100 to both sides:
80x = 680
Dividing both sides by 80:
x = 8.5
So, the consulting engineer worked 8.5 hours.
Now that we know the engineer's time, we can calculate the assistant's time:
Assistant's time = Engineer's time - 5 hours
= 8.5 - 5
= 3.5 hours
Therefore, the consulting engineer worked for 8.5 hours, and the assistant worked for 3.5 hours.
Let's assume that the engineer worked for x hours on the job.
Since the assistant worked 5 hours less than the engineer, the assistant worked for (x - 5) hours on the job.
The engineer's rate is $60 per hour, so the engineer's total bill is 60 * x = $60x.
The assistant's rate is $20 per hour, so the assistant's total bill is 20 * (x - 5) = $20(x - 5).
The customer received a bill for $580, so we can set up the equation:
60x + 20(x - 5) = 580
Simplifying the equation:
60x + 20x - 100 = 580
Combining like terms:
80x - 100 = 580
Adding 100 to both sides of the equation:
80x = 680
Dividing both sides of the equation by 80:
x = 8.5
So, the engineer worked for 8.5 hours on the job.
Now we can find the assistant's time:
(x - 5) = (8.5 - 5) = 3.5
Therefore, the assistant worked for 3.5 hours on the job.
To solve this problem, we can form a system of equations based on the given information.
Let's denote the number of hours the engineer worked as 'E' and the number of hours the assistant worked as 'A'.
From the given information, we know the engineer's time is billed at $60 per hour, so the cost for the engineer is 60E. Similarly, the assistant's time is billed at $20 per hour, so the cost for the assistant is 20A.
According to the problem, the customer received a bill for $580 for the job, so the total cost is 580. We can express this as an equation:
60E + 20A = 580 -----(1)
Additionally, we are told that the assistant worked 5 hours less than the engineer. We can write this as:
A = E - 5 -----(2)
Now we have a system of two equations (equations (1) and (2)).
To solve this system of equations, we can substitute equation (2) into equation (1):
60E + 20(E - 5) = 580
Simplifying this equation, we get:
60E + 20E - 100 = 580
Combining like terms, we have:
80E - 100 = 580
Adding 100 to both sides, we have:
80E = 680
Dividing both sides by 80, we get:
E = 8.5
Now we can substitute the value of E back into equation (2) to find the value of A:
A = 8.5 - 5
A = 3.5
Therefore, the engineer worked for 8.5 hours and the assistant worked for 3.5 hours.
if the engineer worked x hours, the bill is
60x + 20(x-5) = 580
x = 8.5
so, the asst worked 3.5 hours
check:
60*8.5 = 510
20*3.5 = 70