Question

The table shows how the time it takes a train to travel between two cities depends on its average speed.

Answer 1

Answer:

$y=\frac{160}{x}$

Step-by-step explanation:

The table shows how the time it takes a train to travel between two cities depends on its average speed.

function models the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour

y represents the time

and x represents the average speed

WE know distance = speed * times

LEts find the distance using the table

distance = 32* 5= 160

40*4= 160

50*3.2 = 160

Time = distance / speed

times is y , distance is 160  and speed is x

$y=\frac{160}{x}$

Answer 2

Answer:

Option D.

Step-by-step explanation:

Let y represents the time in hours and x be the average speed of train in miles per hour.

We know that

$Time=\frac{Distance}{Speed}$

It means time is inversely proportional to speed.

$y\propto \frac{1}{x}$

$y=\frac{k}{x}$             .... (1)

where, k is the constant of proportionality.

From the given table it is clear that the value of time is y=5 at speed x=32.

Substitute x=32 and y=5 in the above equation to find the value of k.

$5=\frac{k}{32}$

Multiply both sides by 32.

$5\times 32=\frac{k}{32}\times 32$

$160=k$

The value of k is 160.

Substitute k=160 in equation (1).

$y=\frac{160}{x}$

The rational function models $y=\frac{160}{x}$ the time, y, in hours, that it takes the train to travel between the two cities at an average speed of x miles per hour.

Therefore, the correct option is D.