I would like help with this problem please.

Question

Two mechanics worked on a car. The first mechanic worked for 10

hours, and the second mechanic worked for 15

hours. Together they charged a total of $2275

. What was the rate charged per hour by each mechanic if the sum of the two rates was $220

per hour?

Answer 1

Let r1 and r2 be the rates for mechanic 1 and mechanic 2 respectively. Then what we know is:

10 x r1 + 15 x r2 = 2275

and

r1 + r2 = 220

Solve for r1 by eliminating r2:

r2 = 220 - r1 from second equation above. Then in first equation:

10 x r1 + 15 x (220 - r1) = 2275

or

10 x r1 - 15 x r1 = 2275 - (15 x 220)

-5r1 = -1025

r1 = 205

Then

r2 = 220 - r1 = 15

Checking:

10 x 205 + 15 x 15 = 2275