Question

The distance Train A travels is represented by d = 67t, where d is the distance in kilometers and t is the time in hours. The distance Train B travels at various times is shown in the table. What is the unit rate of each train? Which train is going faster?

Time (hours) Distance (km)

2 150

4 300

5 375


Train A's unit rate is--------- km per hour.


Train B's unit rate is---------- km per hour.


which Train is faster?

Answer 1

Train A's unit rate is 67 km per hour.

Train B's unit rate is 75 km per hour.

Train B is faster than Train A

Explanation:

Train A

Distance traveled by Train A is represented by :

`d=67t`

where
`d` represents distance traveled in kilometers and
`t` is the time in hours.

To find the unit rate of Train A, we will plugin
`t=1` and get the distance traveled by Train A in 1 hour which will be the unit rate of Train A in km/hr.

`d=67(1)`

`d=67`

So, distance traveled by Train A in 1 hour = 67 km

∴ Train A's unit rate is 67 km per hour.

Train B

For Train B, we are given the table for the time in hours and distance traveled in that duration.

Taking time =2 hours the distance traveled by Train B= 75 km

To find distance traveled in 1 hour we apply unitary method.

`2\ hr = 150\ km`

So
`1\ hr = (150)/(2)\ km = 75\ km`

So, distance traveled by Train B in 1 hour = 75 km

∴ Train B's unit rate is 75 km per hour.

Difference in units rates =
`75-67=8\ km/hr`

On comparing their unit rate i.e. the speed of the trains we find out that Train B is faster than Train A by 8 km/hr