Question

How much do amber and John earn how many hours it take then and how to they earn all together

Answer 1

(a)

Let Wj be the wages of John and Tj be the time in hours.

If wages and time are proportional, then the relation between them can be expressed as,

`W_j=kT_j`

Here, k is a constant

Rewriting the above equation,

`k=(W_j)/(T_j)`

If the ratio of wages to hours is a constant, then the wages of John is proportional to time.

Taking the ratio of Wj to Tj, we get

`\begin{gathered} k_{}=(18)/(2)=9 \\ _{}k=(27)/(3)=9 \\ k=(36)/(4)=9 \end{gathered}`

Since the ratio of wages to time is a constant, John's wages are proportional to time.

The constant k is the the unit rate. Therefore, the unit rate at which John works is $9/h.

(b)

The graph plotted with Amber's wages against hours worked is a straight line. Therefore, Amber's wages are proportional to time.

The slope of the graph gives the unit rate.

Hence, the unit rate at which Amber work is given by,

`\begin{gathered} \text{Unit Rate=Slope} \\ =(\Delta y)/(\Delta x) \\ =(16-0)/(2-0) \\ =\text{ \$8/h} \end{gathered}`

Therefore, the unit rate at which Amber work is $8/h