Chapter 8.3, Problem 32E

a.

To determine

To draw:

A coordinate plane for each column, and graph the equations in the column on that plane.

Explanation of Solution

Given:

You use a combination of running and walking to complete a race dmiles long. Your running speed is r miles per hour and your walking speed is w miles per hour. Let x be your running time and let y be your walking time (both in hours). Then $rx+wy=d$ .

The table below shows equations of the form $rx+wy=d$ . In each column, one of the values r , w , or d increase while the other two values stay the same.

  

Calculation:

Upon graphing the equation in 1^st column, we will get our required graph as:

  

Upon graphing the equation in 2^ndcolumn, we will get our required graph as:

  

Upon graphing the equation in 3^rdcolumn, we will get our required graph as:

  

b.

To determine

What happens to the graph of $rx+wy=d$ , when running speed increases while walking speed and racing distance stay the same?

Answer to Problem 32E

The graph of $rx+wy=d$ has the same y -interceptsand different x -intercepts.

Explanation of Solution

Given:

You use a combination of running and walking to complete a race dmiles long. Your running speed is r miles per hour and your walking speed is w miles per hour. Let x be your running time and let y be your walking time (both in hours). Then $rx+wy=d$ .

The table below shows equations of the form $rx+wy=d$ . In each column, one of the values r , w , or d increase while the other two values stay the same.

  

Calculation:

Upon looking at the graph of equations in 1^st column, we can see that graph of $rx+wy=d$ becomes more steeper with each increase in running speed r and the y -intercept for each equation is same.

c.

To determine

What happens to the graph of $rx+wy=d$ , when walking speed increases while running speed and racing distance stay the same?

Answer to Problem 32E

The graph of $rx+wy=d$ has the same x -intercepts and different y -intercepts.

Explanation of Solution

Given:

You use a combination of running and walking to complete a race dmiles long. Your running speed is r miles per hour and your walking speed is w miles per hour. Let x be your running time and let y be your walking time (both in hours). Then $rx+wy=d$ .

The table below shows equations of the form $rx+wy=d$ . In each column, one of the values r , w , or d increase while the other two values stay the same.

  

Calculation:

Upon looking at the graph of equations in 2^nd column, we can see that the y -intercept of the graph of $rx+wy=d$ changes as walking speed ( w ) increases while running speed ( r ) and racing distance ( d ) stay the same.

d.

To determine

What happens to the graph of $rx+wy=d$ , when racing distance increases while running speed and walking speed stay the same?

Answer to Problem 32E

Thegraph of $rx+wy=d$ changes x -intercepts and y -intercepts when racing distance increases while running speed and walking speed stay the same.

Explanation of Solution

Given:

You use a combination of running and walking to complete a race dmiles long. Your running speed is r miles per hour and your walking speed is w miles per hour. Let x be your running time and let y be your walking time (both in hours). Then $rx+wy=d$ .

The table below shows equations of the form $rx+wy=d$ . In each column, one of the values r , w , or d increase while the other two values stay the same.

  

Calculation:

Upon looking at the graph of equations in 3^rd column, we can see that the graph of $rx+wy=d$ changes x -intercepts and y -intercepts when racing distance ( d ) increases while running speed ( r ) and walking speed ( w ) stay the same.