Final answer:
Spark is the Hadoop-related Apache project that utilizes an in-memory architecture to run applications faster than MapReduce.
Step-by-step explanation:
The name of the Hadoop-related Apache project that utilizes an in-memory architecture to run applications faster than MapReduce is Spark. Spark is a fast and general-purpose cluster computing system that provides in-memory processing capabilities, making it well-suited for iterative algorithms and interactive data analysis. It offers high-performance data processing and supports various programming languages such as Java, Scala, and Python.