Factory A produces x cars per hour. Factory B produces y cars every 2 hours. How many cars do both factories together produce in 8 hours?

Introduction / Context:
Translate textual rates into per hour rates and aggregate outputs across the specified time window. Then sum outputs from both factories.

Given Data / Assumptions:

• A rate = x cars per hour.
• B rate = y cars every 2 hours = y/2 cars per hour.
• Time window = 8 hours.

Concept / Approach:
Total cars = (rate of A + rate of B) * time. Convert B to per hour first, then multiply by 8 and simplify algebraically.

Step-by-Step Solution:

Verification / Alternative check:
Unit check: both terms have units cars. Factorization 8x + 4y = 4(2x + y) is algebraically correct.

Why Other Options Are Wrong:
8(x + y) incorrectly treats B as y per hour; (8x + y)/2 and 16(x + y) are algebraic or rate conversion errors; 2(4x + y) equals 8x + 2y, which undercounts B by half.

Common Pitfalls:
Forgetting to convert B’s rate to per hour; distributing the 8 incorrectly; misreading parentheses in options.

Final Answer:
4(2x + y)