Question

A student takes a part-time job to earn for summer travel. The number of hours, , the student has to work is inversely proportional to the wage, , in dollars per hour. (a) Write an expression for the function . Note that "" is already provided. Do not include this in your submitted response to this question. MathPAD Response msnViewer_res_c07q_eoc_1_18_mathpad_57_svg ViewEdit (b) How many hours does the student have to work if the job pays an hour

Answer 1

Answer:

(a) $h = \frac{2400}{w}$

(b)300 Hours

(c)150 Hours

(d)Reduced and halved.

(e) $w = \frac{2400}{h}$

Step-by-step explanation:

(a) The number of hours worked is inversely proportional to the wage.

This is written as:

$h \propto \frac{1}{w} \\\text{Introducing variation constant k}\\h = \frac{k}{w}\\ Since the money to be raised is constant, k = \ 2400\\Therefore, h = \frac{2400}{w}$

(b)If the student earns $8 an hour

w=$8

$\text{Number of Hours required, h} = \frac{2400}{8} =300 Hours$

(c)When the wage per hour =$16

When w=$16

$\text{Number of Hours required, h} = \frac{2400}{16} =150 Hours$

The number of hours reduced and is in fact halved.

(d)

$\text{When the wage per hour =w}, h = \frac{2400}{w}\\\text{When the wage per hour =2w}, h = \frac{2400}{2w}=\frac{1}{2} X \frac{2400}{w} =\frac{h}{2}$

The effect of raising the wage from $w to $2w per hour is that the number of hours required to work is reduced and exactly halved.

(e)The wage per hour is inversely proportional to the number of hours.

In fact,

$\text{From h = }\frac{2400}{w}\\\text{Cross Multiplying}\\hw=2400\\\text{Dividing both sides by h}\\w = \frac{2400}{h}$