Problem Solving

Max@Math Revolution wrote:
Which of the following relationships must be inversely proportional to each other?

I. Work done and working time
II. Speed and Traveling Time
III. Profit and Cost

A. I only
B. II only
C. III only
D. II and III
E. I and II

If quantity x and quantity y are inversely proportional to each other, then xy = k where k is a constant.

If x = 3 and y = 8, then k = 24. If we change x to 4, then we have to change y to 6 in order to maintain k to be 24. Thus we see that in an inverse proportion, if one quantity increases, the other quantity decreases and vice versa.

Now let's analyze each Roman numeral.

I. Work done and working time

If we have more working time, we have more work done. We see that one quantity increases and so does the other. This can't be an inverse proportion.

II. Speed and Traveling Time

If we increase our speed, we shorten our traveling time when traveling for a fixed distance. For example, let's say the distance is 120. If speed is 30, then time is 4; if speed is 40, then time is 3. We see that 30 x 4 = 40 x 3 = 120. We see that if one quantity increases then the other quantity must decrease. This is an inverse proportion.

III. Profit and Cost

If we increase the cost, we certainly decrease our profit. However, since profit and cost don't multiply to be a fixed number, they are not in an inversely proportional relationship.

Answer: B