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

How many minutes will it take before both buckets have the same volume of water in them?

Answer 1

By setting up and solving linear equations for the volume of water in each bucket over time, we find that both buckets will have the same volume 7 minutes after they started leaking.

Step-by-step explanation:

To determine how many minutes it will take before both buckets have the same volume of water, we need to establish the rate at which each bucket is leaking. We can do this by setting up two linear equations based on the data given:

• Bucket A starts with 2900 mL and reaches 2000 mL after 10 minutes.
• Bucket B starts with 2725 mL and reaches 2050 mL after 10 minutes.

We can find the rates of change for each bucket as follows:

Rate of change for Bucket A = (2000 mL - 2900 mL) / (10 min - 1 min) = -900 / 9 = -100 mL/min

Rate of change for Bucket B = (2050 mL - 2725 mL) / (10 min - 1 min) = -675 / 9 = -75 mL/min

Now we have two linear equations representing the volumes of buckets A and B over time:

VA(t) = 2900 mL - 100t (Bucket A)

VB(t) = 2725 mL - 75t (Bucket B)

To find the time when the volumes are equal, we set the two equations equal to each other:

2900 - 100t = 2725 - 75t

Solving for t, we get:

175 = 25t

t = 7 minutes

Both buckets will have the same volume 7 minutes after they started leaking.