two mechanics worked on a car the first mechanic worked for 15 hours and the second mechanic worked for 5 hours together they charged a total of 1525 what was the rate charged per hour by each mechanic if the sum of the two rates was 175 per hour

Question

two mechanics worked on a car the first mechanic worked for 15 hours and the second mechanic worked for 5 hours together they charged a total of 1525 what was the rate charged per hour by each mechanic if the sum of the two rates was 175 per hour

Answer 1

Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1000. What was the rate charged per hour by each mechanic if the sum of the two rates was $110 per hour?

Answer 2

Let's assume the rate charged by the first mechanic per hour is "x", and the rate charged by the second mechanic per hour is "y".

We are given two pieces of information:
1. The first mechanic worked for 15 hours, so the total amount charged by the first mechanic is 15x.
2. The second mechanic worked for 5 hours, so the total amount charged by the second mechanic is 5y.

The sum of the two rates is given as 175 per hour. So we can write the equation:
x + y = 175 ------ (Equation 1)

We are also given that the total amount charged by both mechanics is $1525. So we can write another equation:
15x + 5y = 1525 ------ (Equation 2)

Now we can solve the system of equations by substitution or elimination method.

Let's solve by substitution method:
From Equation 1, we can rearrange it as:
x = 175 - y

Now substitute this value of x in Equation 2:
15(175 - y) + 5y = 1525
2625 - 15y + 5y = 1525
-10y = -1100
y = -1100 / -10
y = 110

Now substitute this value of y in the Equation 1 to find x:
x + 110 = 175
x = 175 - 110
x = 65

Therefore, the rate charged per hour by the first mechanic is $65, and the rate charged per hour by the second mechanic is $110.

Answer 3

To find out the rates per hour for each mechanic, we can use a system of equations.

Let's assume the rate per hour for the first mechanic is "x" and for the second mechanic is "y."

According to the given information, the first mechanic worked for 15 hours, so the total amount charged by the first mechanic would be 15x.

Similarly, the second mechanic worked for 5 hours, so the total amount charged by the second mechanic would be 5y.

Now, we are given that the total amount charged by both mechanics together is $1525. So we can set up the equation:

15x + 5y = 1525

Additionally, the sum of the two rates is given as $175 per hour:

x + y = 175

We have a system of two equations:

15x + 5y = 1525 ...(Equation 1)
x + y = 175 ...(Equation 2)

Now we can solve this system of equations.

We can start by solving Equation 2 for x:

x = 175 - y

Substituting this value of x into Equation 1:

15(175 - y) + 5y = 1525

Simplifying the equation:

2,625 - 15y + 5y = 1525

Combining like terms:

-10y = -1,100

Dividing by -10 to get the value of y:

y = -1,100 / -10
y = 110

Now that we have the value of y, we can substitute it back into Equation 2 to find x:

x + 110 = 175

x = 175 - 110
x = 65

Therefore, the rate charged per hour by the first mechanic is $65, and the rate charged per hour by the second mechanic is $110.

Answer 4

If the rates are a and b, then we are told

a+b = 175
15a+5b = 1525

Now just solve for a and b.