Question

Are these two quantities inversely proportional? a.) The time it takes to drive 100 miles and the average driving speed b.) The lengths of sides of a rectangle if the perimeter is fixed c.) The lengths of sides of a rectangle if the are is fixed

Answer 1

A, B & C are inversely proportional.

Explanation:

For two quantities like x and y to be inversely proportional, they are to be written as;

y ∝ 1/x

This means that if x increases, then y decreases and if x decreases, then y increases.

A) The time it takes to drive 100 miles and the average driving speed.

Now, formula for time in motion is;

Time = Distance/speed

Let's denote time as t and speed as v.

Thus;

t = 100/v

From this relationship, it's clear that when v increases, then t decreases and vice versa. Thus it is inversely proportional.

B) The lengths of sides of a rectangle if the perimeter is fixed.

Perimeter of a rectangle is given as;

P = 2(L + W)

Where L is length and W is width.

Now, if the perimeter is fixed, it means an increase in the length will lead to a decrease in the width and vice versa. Thus, it is inversely proportional

C) The lengths of sides of a rectangle if the area is fixed.

If the sides are x & y.

Then;

A = xy

A/x = y

This means that;

1/x ∝ y.

Thus, the sides will be inversely proportional.