Cycling y=1/9

Question

10. Cycling The equation y = 1/9 x represents the distance y, in kilometers, that 9 Patrick traveled in x minutes while training for the cycling portion of a triathlon. The table shows the distance y Jennifer traveled in x minutes in her training. Who has the faster training rate? 

Time (min) 40, 64, 80, 96

Distance (km) 5, 8, 10, 12 

Answer 1

Lets find the slope of the graph for Jennifer's record.  THe slope represents her rate.

 

Slope = (y₂ - y₁) / (x₂ - x₁)

 

 

Lets use the first two points.

 

Slope = (8 - 5) / 64 - 40)

          = 3 / 24

          = 1 / 8

 

 

Use the second and third points.

 

Slope = (10 - 8) / (80 - 64)

         = 2 / 16

         = 1 / 8

 

 

Last points.

 

Slope = (12 - 10) / (96 - 80)

         = 2 / 16

         = 1 / 8

 

 

 

The slopes are constant. 

 

 

Now we compare the slopes.  Use the LCD to compare fractions.

 

1 / 9 = 8 / 72

 

1 / 8 = 9 / 72

 

 

9 / 72 > 8 / 72

 

 

Jennifer has the faster training rate.  She can cover more distance in less time than Patrick can.