Question

An auto shop has two mechanics. They charge a combined rate of per hour. On their most recent car, the first mechanic worked for hours, and the second mechanic worked for hours. Together they charged a total of 1050 . What is the rate charged per hour by each mechanic?

Answer 1

To solve the problem, let's define the variables:

- Let \( r_1 \) be the rate charged per hour by the first mechanic.
- Let \( r_2 \) be the rate charged per hour by the second mechanic.

Suppose the first mechanic worked for \( h_1 \) hours and the second mechanic worked for \( h_2 \) hours. We know from the problem that:

1. The combined charge for their labor is \( 1050 \).
2. Their total charge can be expressed as:
\[
r_1 \cdot h_1 + r_2 \cdot h_2 = 1050
\]

In order to find the rates \( r_1 \) and \( r_2 \), we would also need to know at least one of the following:
- The actual hours \( h_1 \) and \( h_2 \) worked by the two mechanics.
- The rate of one mechanic or the relationship between the two rates.

Could you please provide the hours worked, or any additional information about the rates or their relationship?