Question

Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $3800. What was the rate charged per hour by each mechanic if the sum of the two rates was $215 per hour?

a) First mechanic: $180 per hour, Second mechanic: $35 per hour
b) First mechanic: $160 per hour, Second mechanic: $55 per hour
c) First mechanic: $165 per hour, Second mechanic: $50 per hour
d) First mechanic: $170 per hour, Second mechanic: $45 per hour

Answer 1

Using algebra, we find that the first mechanic charges $115 per hour and the second mechanic $100 per hour. None of the given options match this answer.

Step-by-step explanation:

The question asks to solve for the hourly rates of two mechanics given the total amount charged and the sum of their hourly rates. This is a system of equations problem that can be solved using algebraic methods.

Let's denote the rate of the first mechanic as x dollars per hour and the rate of the second mechanic as y dollars per hour. We have two equations based on the information given:

20x + 15y = 3800 (Total charge equation)

x + y = 215 (Sum of rates equation)

To solve this system, you can multiply the second equation by 15 to facilitate the elimination method:

15x + 15y = 3225

20x + 15y = 3800

Subtracting the first equation from the second gives us:

5x = 575

x = 115

Plugging x back into the second original equation:

115 + y = 215

y = 100

Therefore, the first mechanic charges $115 per hour and the second mechanic charges $100 per hour. This means none of the options (a) through (d) given in the question are correct.