Question

A passenger train's distance traveled is monitored over time. The results are displayed in this table. Time (h) 1 2 3 4 5 Distance traveled (mi) 60 120 180 240 300 What is the constant of proportionality of this proportional relationship? Enter your answer in the box.

Answer 1

You can find the relationship between time and distance given here and then use definition of constant of proportionality to find out the result.

The constant of proportionality of this proportional relationship is 60

What is constant of proportionality?

Firstly, there is proportional relationship.

Two values $x$ and $y$ are said to be in a proportional relationship if

$x = ky$, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

The proportional relationship between x and y can be written symbolically as

$x \propto y$

That middle sign is called sign of proportionality.

There are two things:

First is inversely proportional relationship:

$a \propto \dfrac{1}{b}$

In this, as a increases, b decreases and as b increases, a decreases

secondly, there is directly proportional relationship

$a \propto b$

where if there is increase in a, b increases and if there is increase in b, the value of a increases

How to know what is the constant of proportionality in the given condition?

We can see that when time was 1 hour, the distance traveled was 60,

when time was 2 hour, distance traveled was 120 which

and so on.

We see that in each hour, the distance is increasing by 60.

We can also see that the distance traveled is 60 times the time taken.

or

$\text{distance traveled} = 60 \times \text{time taken}$

Thus, we have

$\text{Distance traveled} \propto \text{time taken}$

and the constant of proportionality is 60 here.

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Answer 2

120 because it’s the square root of 2