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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.
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 distance ( d ) to time ( t ), we first need to determine the speed of the train.
The train travels 420 kilometers in 3 hours. We can calculate the speed using the formula:
[
text{Speed} = frac{text{Distance}}{text{Time}} = frac{420 text{ km}}{3 text{ hours}} = 140 text{ km/h}
]
Now we can express the distance ( d ) as a function of time ( t ). The relationship can be described by the equation:
[
d(t) = 140t
]
where ( d ) 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) = 140t
]
This function indicates that for every hour ( t ), the train travels 140 kilometers.