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A train leaves the station at time t = 0. Traveling at a constant speed, the train travels 390 kilometers in 3 hours. Answer parts a and b.
a. Write a function that relates the distance traveled d to the time t.
The function that relates the distance traveled d to the time t is. (Type an equation.)
To find the function that relates the distance traveled ( d ) to the time ( t ), we can start by calculating the speed of the train.
1. Calculate the speed: The train travels 390 kilometers in 3 hours.
[
text{Speed} = frac{text{Distance}}{text{Time}} = frac{390 text{ km}}{3 text{ hours}} = 130 text{ km/h}
]
2. Write the function: Since the speed is constant, we can express the distance ( d ) as a function of time ( t ):
[
d(t) = 130t
]
where ( d(t) ) is the distance in kilometers and ( t ) is the time in hours.
So, the function that relates the distance traveled ( d ) to the time ( t ) is:
[
d(t) = 130t
]
This means for every hour ( t ) that the train travels, it covers 130 kilometers. If you have additional questions or need further explanation, feel free to ask!