Question

Two mechanics worked on a car. The first mechanic worked for 15 hours, and the second mechanic worked for 5 hours. Together theycharged a total of $1225. What was the rate charged per hour by each mechanic if the sum of the two rates was $135 per hour?

Answer 1

The mechanic who worked for 15 hours charged $55 per hour, while the mechanic that worked for 5 hours charged $80 per hour.

Given:

x = rate of the mechanic who worked 15 hours

y = rate of the mechanic who worked 5 hours

Since the total of their rates is $135, we cuold express it as

x + y = 135

Then, since they are charges a total of $1225 after working, we could express it as

15x + 5y = 1225

Now that we have two expressions:

x + y = 135.................Equation 1

15x + 5y = 1225........Equation 2

We can solve for one variable through substitution

`x+y=135\rightarrow x=135-y`

*Substitute x to the second equation

`15x+5y=1225`
`15(135-y)+5y=1225`

*Solve for y

`2025-15y+5y=1225`
`-15y+5y=1225-2025`
`-10y=-800`

*Divide both sides by -10

`(-10y)/(-10)=(-800)/(-10)`
`y=80`

Now we got a value for y, let us substitute this to the first equation to get the value of x.

`x+y=135`

*Substitute y = 80

`x+(80)=135`
`x+80=135`
`x=135-80`
`x=55`

Now, we got a value for x which is 55.

Going back to our given, since:

x = rate of the mechanic who worked 15 hours

y = rate of the mechanic who worked 5 hours

The mechanic who worked for 15 hours charged $55 per hour, while the mechanic that worked for 5 hours charged $80 per hour.