If it is 9:00 am at the Greenwich Meridian, what is the local time in Los Angeles (longitude 118°W)?

The Earth rotates $15^\circ$ per hour. Los Angeles is at $118^\circ$ West longitude.
The time difference is calculated as:

$$\text{Time difference} = \frac{\text{Longitude difference}}{15^\circ/\text{hour}}$$ $$\text{Time difference} = \frac{118^\circ}{15^\circ/\text{hour}}$$ $$\text{Time difference} = 7 \frac{13}{15} \text{ hours}$$

$$\frac{13}{15} \text{ hours} \times 60 \text{ minutes/hour} = 13 \times 4 \text{ minutes} = 52 \text{ minutes}$$

So, the total time difference is 7 hours and 52 minutes.

Since Los Angeles is West of the Greenwich Meridian, its local time will be earlier than the time at the Greenwich Meridian.
Greenwich time = 9:00 am.

$$\text{Local time at Los Angeles} = \text{Greenwich time} - \text{Time difference}$$ $$\text{Local time at Los Angeles} = 9:00 \text{ am} - 7 \text{ hours } 52 \text{ minutes}$$

To subtract, we can think of 9:00 am as 8 hours and 60 minutes.

$$(8 \text{ hours } 60 \text{ minutes}) - (7 \text{ hours } 52 \text{ minutes}) = 1 \text{ hour } 8 \text{ minutes}$$

Therefore, the local time in Los Angeles is 1:08 am.

The local time at Los Angeles is $\text{1:08 am}$.