Question

The equation y=1/9x represents the distance y, kilometers, that 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?

Answer 1

Answer:

Jennifer has the faster training rate.

Step-by-step explanation:

In order to determine the equation that represents the distance, y (in kilometers), that Jennifer traveled in x minutes:

Choose two ordered pairs from the table: (5, 40) and (64, 8).

Let (x1, y1) = (40, 5)

(x2, y2) = (64, 8)

Substitute these values into the slope formula:

m = (y2 - y1)/(x2 - x1)

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

m = 3/24 = 1/8

Therefore, y = 1/8x represents the distance, y (in kilometers), that Jennifer traveled in x minutes.

In order to find out who has the faster training rate, choose one of the given x values from the table, and substitute it into Patrick's and Jennifer's equations:

Let x = 40:

Patrick:

y = 1/9x

y = 1/9(40)

y = 4.44 km  ⇒ This represents the distance that Patrick traveled in 40 minutes.

In contrast, Jennifer traveled for 5 kilometers in 40 minutes (according to the given table). She reached a farther distance than Patrick, given their training time of 40 minutes.

Therefore, Jennifer has the faster training rate.