Question

A plumber charges an initial amount to make a house call plus an hourly rate for the time he is working. A 1 hour job costs $90 and a 3 hour job costs $210. What is the initial amount and hourly rate that the plumber charges. Show work.

Answer 1

He charges 30 as the intial amount and 60 per hour(60 plus 30 is 90 and 60 times 3 is 180 plus 30 is 210)

Answer 2

The hourly ratio is $60 per hour, and the initial amount charged would be $30.

Explanation:

In this problem, we just have to find the linear relation that model this situation, where the rate would be the slope, and the initial amount would be the y-axis interception. So, basically we have to find the slope-intercept form of this linear relation.

First, we finds the slope using the two given points:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))=(210-90)/(3-1)=(120)/(2)=60`

Now, using one point, the slope and the point-slope form, we have:

`y-y_(1)=m(x-x_(1))\\ y-90=60(x-1)\\y=60x-60+90\\y=60x+30`

Therefore, the hourly ratio is $60 per hour, and the initial charge would be $30.