SOLUTION: a door breaks down 7 times per hour. cost of idle door time is $30 per hour. two carpenters Bob and Bill submit quotes to maintain the doors in the house. Bob charges $21 per hour

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: a door breaks down 7 times per hour. cost of idle door time is $30 per hour. two carpenters Bob and Bill submit quotes to maintain the doors in the house. Bob charges $21 per hour       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 566687: a door breaks down 7 times per hour. cost of idle door time is $30 per hour. two carpenters Bob and Bill submit quotes to maintain the doors in the house. Bob charges $21 per hour and can fix 10 doors per hour while Bill charges $27 and can fix 13 doors per hour. Whose services should be employed?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
door breaks down 7 times an hour and idle time on the door is 30 dollars per hour.
30 dollars per hour idle time equates to 30/60 = .5 dollars per minute.
bob can fix 10 doors an hour.
it takes him 60/10 = 6 minutes per door.
bill can fix 13 doors an hour.
it takes him 60/13 = 4.615384615 minutes per door.
since the door breaks down 7 times an hour, then:
with bob, the total down time per hour would be 7 * 6 = 42 minutes at a cost of .5 dollars per minute for a cost of 21 dollars per hour.
with bill, the total down time per hour would be 7 * 4.615384615 = 32.30769231 minutes at a cost of .5 dollars per minute for a cost of 16.15384615 dollars per hour.
total cost to the company for bob equals 21 + 21 = 42 dollars per hour.
total cost to the company for bill equals 27 + 16.15384615 = 43.15384615 per hour.
it's close, but as long as the door doesn't break down more than 7 times per hour, bob is the cheaper choice.
the equation for the total cost with bob is:
y = 21 + .5 * 6 * x
the equation for the total cost with bill is:
y = 27 + .5 * 4.615384615 * x
thee lines will intersect when x = 8.6666667 for a cost of 47 per hour.
when x is less than 8.6666667, bob is cheaper.
when x is greater than 8.6666667, bill is cheaper.
the graph is shown below:

the line that intersects the y-axis at 27 is bill's equation.
the line that intersects the y-axis at 21 is bob's equation.
the horizontal line at y = 47 shows where the break even point is.