you are paid 1.5 times your normal hourly rate for each hour you work over 35 hours in a week. You work 39 hours this week and earn $678.45. What is your normal hourly rate?

Answer 1

Let's use the variable h to represent our normal hourly rate. Then our increased rate is 1.5h.

The money we earn is always equal to our rate times the # of hours worked at that rate. Since we worked at two different rates, we need to figure out how many hours we worked at each rate. From the problem, we know we can only work up to 35 hours at our normal rate, h. To figure out how many hours we worked at our increased rate (1.5h), we just subtract 35 hours from our total hours worked, as follows:

39 hours - 35 hours = 4 hours

Now we know that we worked 35 hours at the rate of h, and 4 hours at the rate of 1.5h. Using this information and the total money earned that was mentioned in the question ($678.45), we can write an equation:

$678.45 = (35 hours)h + (4 hours)(1.5)h

Since all the values on the right are in terms of h, we can simplify by combining like terms:

$678.45 = (35 hours)h + (4 hours)(1.5)h

$678.45 = (35 hours)h + (6 hours)h

$678.45 = (41 hours)h

Finally, we can solve for h by dividing both sides of the equation by 41:

$678.45/(41 hours) = h

~$16.55/hour = h, rounding to the nearest cent.

In conclusion, our regular hourly rate is approximately $16.55 per hour.