Question

Titus took 30 minutes to walk 2 miles at a constant rate. Let d represent the distance Titus walks in miles after t minutes. What are two different constants of proportionality for the relationship between distance, in miles, and time, in minutes? i need two constants of proportionality.

Answer 1

First, remember the relation:

Distance = Time*Speed.

And a relation of proportionality between X and Y is:

Y = k*X

where k is the constant of proportionality.

First, we know that he needs 30 minutes to walk 2 miles, then we have the relation:

2mi = 30min*speed

Speed = 2mi/30min = (1/15) mi/min.

Then we can represent the relation between d and t in two different ways:

d = (1/15)mi/min*t

where the constant is = (1/15)mi/min and this means that in one minute, he walks 1/15 of a mile.

The other way of writing this is obtained by dividing at both sides by (1/15)mi/min:

t = 15min/mi*d

Now the constant is 15min/mi, which means that when he walks on mile, 15 minutes of time passes by.

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