Chapter ISG, Problem 3.2.1P

a.

To determine

To complete the table and form a graph

Explanation of Solution

Given information:

The charity walk is 25.5km long.

J’s speed is, constant through-out the race, at 4.25km per hour.

Concept Used:

Equation making and solving

Graph:

  

Calculation:

Let, the number of hours be “x”

Therefore, the equation will be,

  $y=25.5-4.25x$

Where, x is the time

y is the distance.

Hence, the table is,

x	y=25.5-4.25x	y	(x,y)
1	25.5-(4.25x1)	21.25	(1, 21.25)
2	25.5-(4.25x2)	17	(2, 17)
3	25.5-(4.25x3)	12.75	(3, 12.75)

b.

To determine

To evaluate x and y- intercept.

Answer to Problem 3.2.1P

x-intercept shows the total time she took and the y-intercept shows the total distance.

Explanation of Solution

Given information:

The equation is 1y $y=25.5-4.25x$

  

Concept Used:

Graph evaluation

Calculation:

The x-intercept is the point where the line touches the x-axis. In this situation it shows the total time J takes to complete the race.

The y- intercept is the point where the line touches the y-axis. In this situation it shows the total distance J has to travel.

Conclusion:

x-intercept shows the total time she took and the y-intercept shows the total distance.

c.

To determine

To calculate the time it will take her, if she has walked 17km

Answer to Problem 3.2.1P

It will take her 4 hours more to complete the race.

Explanation of Solution

Given information:

  

Concept Used:

Graph reading.

Calculation:

Concluding from the graph, the point where J has completed 17km, that is, y is 17, is

  $(2,17)$

Therefore, Time she took to reach 17km is,

  $=2hours$

Time she will take to complete the race now= total time- time at 17km

Substituting the values,

  $=6-2$

On solving,

  $=4hours$

Therefore, it will take her 4 hours more to complete the race.

Conclusion:

It will take her 4 hours more to complete the race.

d.

To determine

To evaluate the given situation

Answer to Problem 3.2.1P

This new equation cannot give the solution

Explanation of Solution

Given information:

The equation is $y=25.5-4.25x$

Replacing the constant with 8.5

Concept Used:

Equation evaluation

Graph:

  

Calculation:

Substituting the new constant in the equation,

  $y=8.5-4.25x$

Forming the graph of this equation,

Concluding from the graph,

Total distance she has to travel is 8.5km

And time taken is 2hours.

Therefore, using this equation Reza would have not found the solution.

Conclusion:

This new equation cannot give the solution