Question

An electrician charges $70 for a job which takes two hours to complete and $92.50 for 3.5 hours of work.
a.) Find a linear model to express the charge, $C, for t hours of work.

Answer 1

Since the rates describe vary, we use the harmonic mean:
$$
C={t\over {2\over70}+{3.5\over92.50}}~dollars
$$

Answer 2

im sorry, i still dont understand

Answer 3

You can think of the problem like this

It takes \({2\over 70}\) hours per $ for the 1st job
The second takes \({3.5\over 92.50}\) hours per $ for the second job

If done concurrently, these jobs can would take \({2\over 70} +{3.5\over 92.50}\) hours per $, which would take \({1\over C}\) hours per $ if done together:
$$
{2\over 70} +{3.5\over 92.50}={1\over C}\\
\implies C={1\over {2\over70}+{3.5\over92.50}} \text{dollars per hour}
$$
So in t hours, the cost would be
$$
C\times t~dollars
$$

Answer 4

okay i understand now. thank you very much.

Answer 5

you're welcome