SOLUTION: uestion Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. Together they charged a total of $ 975

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Question 1154036: uestion

Two mechanics worked on a car. The first mechanic worked for
10
hours, and the second mechanic worked for
5
hours. Together they charged a total of
$
975
. What was the rate charged per hour by each mechanic if the sum of the two rates was
$
120
per hour?
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
Let M1 charge at x dollars per hour and M2 at y dollars per hour
x+%2B+y+=+120 ---> (1)
Charge for M1 working for 10 hours = 10x
Charge for M2 working for 5 hours = 5y
Total charge is given to be 975, so
10x+%2B+5y+=+975 ---> (2)
So we have 2 simultaneous equations in 2 variables which can be easily solved.
Multiply (1) by 10 to get
10x+%2B+10y+=+1200 ---> (3)
Subtract (2) from (3) to get
5y+=+1200+-+975+=+225
So y+=+225%2F5+=+45
From (1) we solve for x
x+=+120+-+y+=+120+-+45+=+75
Check:
For 10 hours, M1 will get 10*75 = $750
For 5 hours, M2 will get 5*45 = $225
Total = $750 + $225 = $975 which matches the problem input. Check complete!

Ans:
Mechanic 1 charges $75 per hour
Mechanic 2 charges $45 per hour