Question

At a lical train station 3 trains are scheduled to leave the station every 48 minutes.

1) Write a constant of proportionality equation for this relationship.

2) Given the relationship is the same, how many minute have passed after 10 trains have left the station?

3) Given the relationship is the same, how many trains have left the station after 8 hours?

Answer 1

Part 1)
`k=(1)/(16)\ (trains)/(min)`

Part 2)
`160\ min`

Part 3)
`30\ trains`

Explanation:

Part 1) Write a constant of proportionality equation for this relationship

Let

y ----> the number of trains

x ----> the time minutes

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In this problem we have

For x=48 min, y=3 trains

`k=y/x` ---->
`k=(3)/(48)`

Simplify

`k=(1)/(16)`

The units of the constant of proportionality are
`(trains)/(min)`

so

`k=(1)/(16)\ (trains)/(min)`

The linear equation is

`y=(1)/(16)x`

Part 2) Given the relationship is the same, how many minute have passed after 10 trains have left the station?

For y=10 trains

substitute the value of y in the equation and solve for x

`10=(1)/(16)x`

`x=10(16)=160\ min`

Part 3) Given the relationship is the same, how many trains have left the station after 8 hours?

For x=8 hours

substitute the value of x in the equation and solve for y

But first convert hours to minutes

remember that

`1\ h=60\ min`

`8\ h=8(60)=480\ min`

substitute

`y=(1)/(16)(480)=30\ trains`