Value Mixture problems

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
$1375
. What was the rate charged per hour by each mechanic if the sum of the two rates was
$165
per hour?

Answer 1

rate charged by 1st mechanic = x

rate charge by 2nd mechanic = y

 

x+ y = 165

 

15x + 5y = 1375

 

now solve the system of linear equation to find rate charged per hour by each mechanic

Answer 2

15X + 5Y = 1375

 

X + Y = 165 --> y = 165 - X

 

15X + 5 ( 165 - x) = 1375

 

15X + 825 - 5X - 1375

 

10X = 550

 

X=55

 

Y  = 165 - 55 = 110

 

 

15*55 + 5 x 110 = 825 + 550 =1375

 

One mechanic charges $55 per hour while the other charges

$110 per hour, or twice as much.

 

Why?