To solve this problem, let's break it down step by step:

Step 1: Convert hours to minutes.

Since the leak rate is given in quarts per minute, we first need to convert the time from hours to minutes.

$4 \text{ hours} = 4 \times 60 = 240 \text{ minutes}$

Step 2: Calculate the total volume of oil leaked.

The leak rate is 0.8 quarts per minute. Over 240 minutes, the total volume of oil leaked is:

$\text{Volume leaked} = 0.8 \text{ quarts/minute} \times 240 \text{ minutes} = 192 \text{ quarts}$

Step 3: Convert the leaked volume from quarts to gallons.

There are 4 quarts in a gallon, so:

$\text{Volume leaked in gallons} = \frac{192 \text{ quarts}}{4 \text{ quarts/gallon}} = 48 \text{ gallons}$

Step 4: Calculate the remaining volume of oil in the barrel.

The barrel initially contains 160 gallons. After losing 48 gallons, the remaining volume is:

$\text{Remaining volume} = 160 \text{ gallons} - 48 \text{ gallons} = 112 \text{ gallons}$

Thus, 112 gallons of oil will be left in the barrel after 4 hours.

Would you like more details on any part of the solution? Here are some related questions to consider:

1. What is the significance of converting quarts to gallons in this context?
2. How would the remaining volume change if the leak rate doubled?
3. If the barrel was only half full initially, how much oil would be left after 4 hours?
4. How long would it take for the entire barrel to empty at the same leak rate?
5. What if the leak started after the first hour? How much oil would be left?

Tip: Always ensure your units are consistent when performing calculations to avoid errors.