A train leaves the station at time t = 0. Traveling at a constant speed, the train travels 420 kilometers in 3 hours. Answer parts a and b.

To find the function that relates distance traveled ( d ) to time ( t ), we start by determining the speed of the train.

1. Calculate the speed:

– Distance = 420 kilometers

– Time = 3 hours

– Speed = Distance / Time = ( frac{420 text{ km}}{3 text{ hours}} = 140 text{ km/h} )

2. Write the function:

The distance ( d ) is equal to the speed of the train multiplied by the time ( t ). Therefore, we can express this relationship with the equation:

[

d(t) = 140t

]

where ( d(t) ) is the distance in kilometers and ( t ) is the time in hours.

This equation shows that for every hour ( t ) that the train travels, it covers 140 kilometers.

Let me know if you need help with part b!