Question

A service technician charges $30 up front andC$46 for each hour that he works.

What will a 4-hour job cost?

Answer 1

a. A 4-hour job costs $214. b. If the technician works 2 days, averaging 6 hours/day, the overall cost is $612. c. For costs of $76, $513, and $1000, the technician worked approximately 1.17 hours, 10.76 hours, and 21 hours (rounded).

a. Cost of a 4-hour Job:

-
`\(30 + (4 * 46) = 30 + 184 = 214\)`

- A 4-hour job will cost $214.

b. Overall Cost for 2 Days (6 hours per day):

-
`\(2 * (30 + (6 * 46)) = 2 * (30 + 276) = 2 * 306 = 612\)`.

- The overall cost for two days, averaging 6 hours per day, is $612.

c. Finding Hours Worked for Given Costs:

i.
`\(76 = 30 + (x * 46)\)`.

- Solve for x:
`\(x = (76 - 30)/(46) \approx 1.17\)` hours.

ii. 513 = 30 + (x × 46).

- Solve for x:
`\(x = (513 - 30)/(46) \approx 10.76\)` hours.

iii. 1000 = 30 + (x × 46).

- Solve for x:
`\(x = (1000 - 30)/(46) \approx 20.87\)` hours.

- Rounded to the nearest half hour,
`\(x \approx 21\)` hours.

Therefore, for the given costs:

i.
`\(x \approx 1.17\)` hours,

ii.
`\(x \approx 10.76\)` hours, and

iii.
`\(x \approx 21\)` hours.

The complete question is:

A service technician charges $30 up front and $46 for each hour that he works.

a. What will a 4-hour job cost?

b. If the technician works on a job for 2 days and averages 6 hours per day, what will be the overall cost?

c. Find how many hours the technician worked if the cost is:

i. $76

ii. $513

iii. $1000 (round to the nearest half hour).