word problem

Question

Both of the following Heating & Cooling companies charge a service call fee and an hourly rate, for residential service.
For Schneider's Heating & Cooling Service, a 5 hour service costs $170 and a 2 hour service costs $92
For Johnson's Heating & Cooling Service, a 5 hour service costs $174 and a 2 hour service costs $114
For each company, find a linear model for the relationship between the hours spent on a repair and the total charges of a repair. Let, x represent the number of hours of service and C represent the cost of the service

 

The linear model for Schneider's Heating & Cooling Service: C=?

The linear model for Johnson's Heating & Cooling Service:C=?

 

The services of these companies would cost the same for a ____?hour service. (round to the nearest tenth of an hour)

Answer 1

We have 2 data points for each company.

 

Schneider's:  (2, 92), (5, 170)

Find the slope

m = (170-92)/(5-2) = 78/3 = 26

C = 26x + b

Use one of the points given as (x,y) to solve for b

92 = 26(2) + b

b = 40

C = 26x + 40

 

Scnheider's charges $26 per hour plus a base fee of $40

 

Follow the same steps to find the linear model for Johnson's

 

Once you have both linear models, set the 2 equations equal

to each other and solve for x to find the number of hours of

work that would cause the costs to be the same