Question

Two buckets, each with a different volume of water, start leaking water at the same time, but at different rates. Assume the volumes are changing linearly.

Bucket Volume (mL)
Time (min) Bucket A Bucket B
1 2,900 2,725
10 2,000 2,050

What was the difference, in milliliters, of their starting volumes? Do not include units in your answer?

Answer 1

The difference in the starting volumes of Bucket A and Bucket B is 200 mL. This was determined by calculating the rate at which each bucket leaked water and extrapolating back to the initial starting point.

Step-by-step explanation:

To find the starting volumes of the two buckets and their difference in milliliters, we will calculate the rate at which each is leaking and then extrapolate backward to when the leaking started, which is time zero. Bucket A goes from 2,900 mL to 2,000 mL over 9 minutes (from minute 1 to minute 10), meaning it leaks 900 mL in 9 minutes or 100 mL/minute. Similarly, Bucket B goes from 2,725 mL to 2,050 mL over the same period, so it leaks 675 mL in 9 minutes or 75 mL/minute.

At 1 minute, Bucket A had 2,900 mL, accounting for the loss, it must have started with 2,900 mL + 100 mL, which equals 3,000 mL. Similarly, Bucket B had 2,725 mL at 1 minute, which means it started with 2,725 mL + 75 mL, totaling 2,800 mL.

The starting volume difference is therefore 3,000 mL (Bucket A's starting volume) minus 2,800 mL (Bucket B's starting volume), which equals 200 mL. Hence, the starting volumes of the buckets differed by 200 mL.