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Video: Solving Word Problems Involving Rate of Change

Bethani Gasparine

At 5:00, the water level in a pool reaches a height of 10 inches. At 8:00, the water level is at 50 inches. What is the rate of change of the water level per minute?

02:03

Video Transcript

At five o’clock, the water level in a pool reaches a height of 10 inches. At eight o’clock, the water level is at 50 inches. What is the rate of change of the water level per minute?

To find the rate of change of the water level per minute, we need to find the change in the water level, which is in inches, and put it over the change in the time, which is in minutes. We went from 10 inches at five o’clock to 50 inches at eight o’clock. Let’s go ahead and take a closer look at the time because we need that time in minutes. Five o’clock is when it began, so zero minutes have went by. Once we get to eight o’clock, three hours have went by. But how many minutes is that?

Since there are 60 minutes in one hour and three hours went by, so we need to multiply by three hours. So 60 times three means 180 minutes have went by. So let’s replace three hours with 180 minutes.

So we need to look at the change in the inches and the change in the minutes. So to go from 10 inches to 50 inches, there’s a change of 40 inches because 50 minus 10 is 40. To go from zero minutes to 180 minutes, that’s a change of 180 minutes; 180 minus zero is 180.

This fraction can be reduced because 40 and 180 are both divisible by 20; they have a common factor of 20. So this reduces to two inches per, every, nine minutes.

Therefore, the rate of change of the water level per minute would be two-ninths of an inch per minute.