SOLUTION: Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $70 per hour. The mechanics worked for a combined total of 20 hours, and tog

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $70 per hour. The mechanics worked for a combined total of 20 hours, and tog      Log On


   

Question 1185896: Two mechanics worked on a car. The first mechanic charged $65 per hour, and the second mechanic charged $70 per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1375. How long did each mechanic work?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
first and second mechanics
x and y, their time each
or
h, time for second mechanic @ $70 per hour
20-h, time for first mechanic @ $65 per hour

70h%2B65%2820-h%29=1375


70h-65h%2B65%2A20=1375
%2870-65%29h=1375-65%2A20
h=%281375-%2865%29%2820%29%29%2F%2870-65%29--------Simplify, compute this.

--
h=%281375-1300%29%2F5
h=75%2F5
highlight%28h=15%29

check: found h reproduce the $1375?
15 hours at $70/hr
5 hours at $65/hr
15%2A70%2B5%2A65
1375yes

Answer by greenestamps(13214) About Me  (Show Source):
You can put this solution on YOUR website!


Informally....

$1375 for 20 hours of work is $67.50 per hour, which is exactly halfway between $65 and $70 per hour. So the two mechanics worked equal numbers of hours.

ANSWER: each mechanic worked 10 hours.

CHECK: 10(65)+10(70)=650+700=1350