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The distance Train A travels is represented by d = 69t, 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?

The distance Train A travels is represented by d = 69t, where d is the distance in-example-1
User Hoefling
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2 Answers

4 votes

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d(A) = 69t


d(B) = 75t

The unit rate is the coefficient of t which is the slope of the line because the trains distance traveled equation are linear.

Thus :

Train A's unit rate is 69 km per hour.

And

Train B's unit rate is 75 km per hour.

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Train B is going faster because its unit rate is greater than Train A's unit rate .

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User RishiD
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3 votes

If d is distance measured in km and t is time measured in hours, then d = 69t tells you that train A is moving at a rate of 69 km/h.

Why? If t = 1, then d is the distance it moves in 1 hour, and that's precisely the unit rate. It's the rate at which the distance changes when 1 unit of time passes.

For train B, use the info in the given table. In 1 hour (between hours 4 and 5), the train covers a distance of 375 km - 300 km = 75 km. So it's moving at a rate of 75 km/h.

It should be clear which train is faster.

User Kingsolmn
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