Angela is on her way from home from Jersey City into New York City for dinner. She walks 1 mile to the train station, takes the train 1/2 of the way, and takes a taxi 1/6 of the way to the restaurant. How far does Angela live from the restaurant?

Assuming the restaurant is in NYC, that means that if the whole distance is x,

1 + x/2 + x/6 = x

30 miles

To find the total distance Angela lives from the restaurant, we need to add up the distances she walked, took the train, and took the taxi.

First, let's find the distance she walked from home to the train station. Angela walks 1 mile.

Next, let's find the distance she took the train. The train covers 1/2 of the total distance. To find this distance, we can multiply the total distance by 1/2: 1 mile * 1/2 = 1/2 mile.

Then, let's find the distance she took the taxi. The taxi covers 1/6 of the total distance. To find this distance, we can multiply the total distance by 1/6: 1 mile * 1/6 = 1/6 mile.

To find the total distance Angela lives from the restaurant, we add up the distances: 1 mile + 1/2 mile + 1/6 mile = 1 2/3 miles.

Therefore, Angela lives approximately 1 2/3 miles from the restaurant.

To determine the distance Angela lives from the restaurant, we need to calculate the total distance she traveled.

Let's break down the distances she covered:

1. Distance walked to the train station: Angela walks 1 mile.
2. Distance traveled by train: Angela takes the train for 1/2 of the way. We need to find out what fraction of the total distance that represents.
3. Distance traveled by taxi: Angela takes a taxi for 1/6 of the way. Again, we need to determine the fraction of the total distance it represents.

Once we have the fractions of the total distance, we can add them up to find the total distance traveled.

To calculate the total distance, let's assume the distance from Angela's home to the restaurant is x miles.

1. Distance walked to the train station: 1 mile.
2. Distance traveled by train: Angela takes the train for 1/2 of the way, so the distance traveled by train is (1/2) * x.
3. Distance traveled by taxi: Angela takes a taxi for 1/6 of the way, so the distance traveled by taxi is (1/6) * x.

Now we can add up the distances:

Total distance = Distance walked + Distance traveled by train + Distance traveled by taxi

Total distance = 1 mile + (1/2) * x + (1/6) * x

To find the final answer, we need to simplify this expression:

Total distance = 1 + (1/2)x + (1/6)x

Combining the fractions:

Total distance = 1 + (3/6)x + (1/6)x

Total distance = 1 + (4/6)x

To simplify, we can simplify the fraction (4/6) to (2/3):

Total distance = 1 + (2/3)x

So, Angela lives a distance of 1 + (2/3)x miles from the restaurant.