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 km per hour.

train b's unit rate km per hour.

which train is faster?

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

Step-by-step explanation:

Train A

Distance traveled by Train A is represented by :

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

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

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.

So

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 =

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