Question

Two mechanics worked on a car. The first mechanic charged $75

per hour, and the second mechanic charged $95
per hour. The mechanics worked for a combined total of 20
hours, and together they charged a total of $1800
. How long did each mechanic work?

Answer 1

The first mechanic worked 5 hours

The second mechanic worked 15 hours

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Work Shown:

x = number of hours the 1st mechanic worked

y = number of hours the 2nd mechanic worked

75x = total amount charged by the 1st mechanic

95y = total amount charged by the 2nd mechanic

75x+95y = total charged both mechanics combined

75x+95y = 1800 is the first equation to set up

The other equation is x+y = 20 since the total combined time spent was 20 hours.

Solve for y to get y = 20-x

Then plug it into the first equation to solve for x.

75x+95y = 1800

75x+95( y ) = 1800

75x+95(20-x) = 1800 ....... replace y with 20-x

75x+1900-95x = 1800

-20x+1900 = 1800

-20x = 1800-1900

-20x = -100

x = -100/(-20)

x = 5

Now we can determine the value of y

y = 20-x

y = 20-5

y = 15

The first mechanic worked 5 hours.

The second mechanic worked 15 hours.