Let's denote the distance between Albany and Syracuse as \( D \) miles.

For the first part of the trip, from Albany to Syracuse, the train travels at an average speed of 40 mph. The time taken for this part of the trip can be calculated using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

So, the time taken to travel from Albany to Syracuse is:

\[ \text{Time}_{\text{Albany to Syracuse}} = \frac{D}{40} \]

For the return trip, from Syracuse back to Albany, the train travels at an average speed of 49.99999999999999 mph (which we can round to 50 mph for practical purposes). The time taken for this part of the trip is:

\[ \text{Time}_{\text{Syracuse to Albany}} = \frac{D}{50} \]

The total traveling time is given as 5 hours and 24 minutes. To convert this to hours, we have:

\[ 5 \text{ hours} + \frac{24}{60} \text{ hours} = 5 + 0.4 \text{ hours} = 5.4 \text{ hours} \]

The sum of the times for both parts of the trip should equal the total traveling time:

\[ \frac{D}{40} + \frac{D}{50} = 5.4 \]

To solve for \( D \), we need to find a common denominator for the fractions on the left side of the equation. The common denominator for 40 and 50 is 200. So we can rewrite the equation as:

\[ \frac{5D}{200} + \frac{4D}{200} = 5.4 \]

Combining the fractions, we get:

\[ \frac{9D}{200} = 5.4 \]

Now, we can solve for \( D \) by multiplying both sides of the equation by 200/9:

\[ D = 5.4 \times \frac{200}{9} \]

\[ D = 5.4 \times \frac{200}{9} \]

\[ D = 5.4 \times 22.22222222222222 \]

\[ D = 120 \]

So, the distance between Albany and Syracuse is 120 miles.
올버니와 시라큐스 사이의 거리를 \( D \) 마일로 표시해 보겠습니다.

여행의 첫 번째 부분인 올버니에서 시라큐스까지 기차는 평균 시속 40마일의 속도로 이동합니다. 이 부분의 소요 시간은 다음 공식을 사용하여 계산할 수 있습니다:

\[ \text{시간} = \frac{\text{거리}}{\text{속도}} \]

따라서 올버니에서 시라큐스까지 이동하는 데 걸리는 시간은 다음과 같습니다:

\[ \text{시간}_{\text{올버니에서 시라큐스}} = \frac{D}{40} \]

시라큐스에서 올버니로 돌아가는 왕복 구간에서는 기차가 평균 시속 49.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999