Questions: In auto shop has two mechanics. They charge a combined rate of 195 per hour. On their most recent car, the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of 3400. What is the rate charged per hour by each mechanic? First mechanic: per hour Second mechanic: per hour

In auto shop has two mechanics. They charge a combined rate of 195 per hour. On their most recent car, the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of 3400. What is the rate charged per hour by each mechanic? First mechanic: per hour Second mechanic: per hour
Transcript text: In auto shop has two mechanics. They charge a combined rate of $\$ 195$ per hour. On their most recent car, the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $\$ 3400$. What is the rate charged per hour by each mechanic? First mechanic: $\$ \square$ per hour Second mechanic: $\$ \square$ per hour
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Solution

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Solution Steps

Step 1: Formulate the Equations

Given the total charge \(C = 3400\) and the combined rate \(R = 195\), we can formulate the following equations:

  1. \(h_1r_1 + h_2r_2 = 3400\)
  2. \(r_1 + r_2 = 195\)
Step 2: Solve the System of Equations

Using the system of linear equations, we solve for \(r_1\) and \(r_2\). The solution gives us \(r_1 = 95\) and \(r_2 = 100\).

Final Answer:

The rate charged per hour by the first mechanic is \(r_1 = 95\) and by the second mechanic is \(r_2 = 100\).

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