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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 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!