two mechanics worked on a car. The first mechanic worked for 10 hrs, and the second mechanic worked for 5 hours. Together they charged a total of $1475. What was the rate charged per hour by mechanic if the sum of the two rates was $190 per hour? What is the first mechanic make per hour? And what did the second mechanic make per hour?

Answer:

The first mechanic $90/hour and the second charged $70/hour

Step-by-step explanation:

Lets start off by letting x be the first mechanics rate and y being the second mechanics rate. We know that the first mechanic worked 5 hours and that the second mechanic worked 10 hours and together they charged 1150. An equation to express this would be:

5x+10y = 1150

We also know that together they charged 160/per hour. An equation to express this would be:

x+y = 160

Now we can solve the second equation for x or the first mechanics rate.

x+y = 160

x = 160 - y

Now that we have an expression for x we can plug that back into the first equation and solve for y or how much the second mechanic charged.

5x+10y=1150 plug in x =160-y

5(160-y)+10y=1150 Distribute

800 -5y+10y = 1150 Combine like terms

800 +5y = 1150 Subtract 800 from both sides

5y = 350 divide by 5

y = 70

So we know that the second mechanic charged $70/hour. We also know that(from our work before) that the first mechanic charges $160 - the rate the second mechanic charged. We know that's $70/hour so we can plug in and solve for the first rate.

x = 160-y

x = 160-70

x = 90

So we know that the first mechanic charged $90/hour and the second mechanic charged $70/hour.

Final answer:

The rate per hour for the first mechanic is $105 and for the second mechanic is $85.

Explanation:

This problem is a case of simultaneous equations where we need to determine the rates at which the two mechanics charge. Let's denote the hourly rates of the first and second mechanics as x and y respectively. From the question, we know:
1. x + y = $190 (The sum of the two rates was $190 per hour)
2. 10x + 5y = $1475 (The first mechanic worked for 10 hours and the second mechanic worked for 5 hours, and together they charged a total of $1475)

To solve these equations, you can start by multiplying the first equation by 5 to match the second equation:
5x + 5y = $950

Now, subtract this from the second equation:
10x - 5x = $1475 - $950
5x = $525

Therefore, x ($/hour by the first mechanic) = $525 / 5 = $105

You can now substitute x = $105 into the first equation to get:
$105 + y = $190
Therefore, y ($/hour by the second mechanic) = $190 - $105 = $85

Learn more about Simultaneous equations here:

brainly.com/question/31913520

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