Final answer:
Using the average velocity of the Pacific plate's northwest movement (6 cm/year) relative to the North American plate, it is estimated that it would take approximately 98.3 million years for Los Angeles to reach the same latitude as San Francisco, assuming a constant motion to cover the 590 km displacement.
Step-by-step explanation:
The question asks how far in the future Los Angeles, which is west of the San Andreas fault, will reach the same latitude as San Francisco, which is east of the fault, assuming a constant displacement rate.
The rate at which the land west of the San Andreas fault is moving is about 6 cm/year northwest relative to the land on the east. To find the time it will take for a displacement of 590 km northwest, we convert the distance to centimeters (590,000,000 cm) and divide it by the rate of movement (6 cm/year).
This results in approximately 98,333,333.33 years for Los Angeles to reach the same latitude as San Francisco if the motion remains constant.