Question

Roberto is having his house painted. The job takes three days, and he pays the painter the same hourly rate
every day. The cost of the job is in the chart below.
Hours worked
Amount paid
Day 1
5
$300
Day 2
4
$240
Day 3
6
$360
What is the painter's unit rate of change of dollars with respect to time; that is, how much is the painter paid for
one hour worked?

Answer 1

Answer:

$\ 60\ per\ hour$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x -----> the number of hours worked

y ----> the amount paid in dollars

In this problem we have a proportional variation, between two variables, x, and y

Find out the constant of proportionality k

For (5,300) -----> $k=y/x$ ----> $k=300/5=60\ \ /h$

For (4,240) -----> $k=y/x$ ----> $k=240/4=60\ \ /h$

For (6,360) -----> $k=y/x$ ----> $k=360/6=60\ \ /h$

The constant k is

$k=60\ \ /h$

The equation is equal to

$y=60x$

The unit rate of change of dollars with respect to time is equal to the constant of proportionality or slope of the linear equation

therefore

$\ 60\ per\ hour$

Answer 2

Answer:

P = 65H and P=70H

Step-by-step explanation:

They both are greater then P=60H