Chapter ISG, Problem 4.4.2P

a.

To determine

To graph the given data.

Explanation of Solution

Given information:

The works and number of minutes they will take to finish job is,

Workers	Minutes
9	80
16	40
18	35
8	90
15	60
11	60
9	70
17	30
9	70
15	50
11	80
12	70

Graph:

  

b.

To determine

To draw a line to fit to show the trend

Explanation of Solution

Given information:

The works and number of minutes they will take to finish job is,

Workers	Minutes
9	80
16	40
18	35
8	90
15	60
11	60
9	70
17	30
9	70
15	50
11	80
12	70

Graph:

  

c.

To determine

To write the equation of line.

Answer to Problem 4.4.2P

The equation of line is $y=7x-55$

Explanation of Solution

Given information:

The graph is,

  

Formula used:

Equation of line in slope intercept form,

  $y=mx+c$

Equation of line in slope point form,

1 $y-y1=m(x-x1)$

Slope is,

3 $m=\frac{y2-y1}{x2-x1}$

Calculation:

Let the two points be,

(9, 8) and (15, 50).

Substituting the values in the formula of slope,

  $m=\frac{50-8}{15-9}$

So,

  $m=\frac{42}{6}$

On solving,

  $m=7$

Hence, slope is 7.

Substituting the values in the equation of line in slope point form,

  $y-50=7(x-15)$

Converting it into slope intercept form,

Opening the brackets,

  $y-50=7x-105$

Shifting left hand side value to right hand side,

  $y=7x-105+50$

On solving,

  $y=7x-55$

Hence, the equation of line in slope-intercept form is,

  $y=7x-55$

Conclusion:

The equation of line is $y=7x-55$

d.

To determine

To calculate how long the workers will take to complete the task.

Answer to Problem 4.4.2P

A group of 6 workers will finish the work in 95mins.

Explanation of Solution

Given information:

Number of workers are 6.

Graph for the given data is,

  

Formula used:

Graph evaluating.

Calculation:

Checking the value of “y” in the graph when “x” is 6

Concluding from the graph,

When $x=6$ , then,

  $y=95\min$

Hence, a group of 6 workers will finish the work in 95mins.

Conclusion:

A group of 6 workers will finish the work in 95mins.

e.

To determine

To number of workers needed

Answer to Problem 4.4.2P

14 workers are required to complete work in 45 mins.

Explanation of Solution

Given information:

The time in which the work should be finished is 45mins

The equation of line is $y=7x-55$

The graph is,

  

Formula used:

Substitution and equation solving.

Calculation:

Substituting the value in the equation,

  $45=7x-55$

Shifting right hand side values to left hand side,

  $7x=45+55$

On solving,

  $7x=100$

Cross- multiplying both sides,

  $x=\frac{100}{7}$

On solving,

  $x=14.28$

Rounding off,

  $\approx 14$

Hence, 14 workers are required to complete work in 45 mins.

Conclusion:

14 workers are required to complete work in 45 mins.

f.

To determine

To calculate the y-intercept

Answer to Problem 4.4.2P

The y- intercept is -55.

Explanation of Solution

Given information:

The equation for the given data set is $y=7x-55$

Formula used:

Equation of line is,

  $y=mx+c$

Where, m is slope

c is y-intercept

Calculation:

Comparing with the equation of line and the equation of the given data set,

The y- intercept is,

  $c=-55$

The y-intercept in this situation tells the total time it will take for 0 workers to do the work.

From the equation the value of y- intercept is negative, which should have been positive, because the time cannot be negative.

Conclusion:

The y- intercept is -55.