One girl can eat 112 chocolates in half a minute, while her boyfriend can eat half as many chocolates in twice the time. If they both start eating at the same time and continue at these constant rates, how many chocolates can they eat together in 12 seconds?

Introduction / Context:
This question is about combined rates of eating chocolates. Two people have different speeds of eating, and we are told how many chocolates each can eat over specific times. We then need to find how many chocolates they can eat together in a shorter time interval when both eat simultaneously.

Given Data / Assumptions:

• The girl can eat 112 chocolates in half a minute, that is in 30 seconds.
• The boy can eat half as many chocolates, which is 56 chocolates, in twice the time, which is one minute or 60 seconds.
• Both eat at constant speeds over time.
• We are asked how many chocolates they can eat together in 12 seconds.

Concept / Approach:
We first convert the information about how many chocolates are eaten in given times into per second rates for each person. After that we add the two rates to get a combined rate in chocolates per second. Finally, we multiply this combined rate by the required time interval of 12 seconds to obtain the total number of chocolates eaten together.

Step-by-Step Solution:
Girl's rate: 112 chocolates in 30 seconds. So her rate = 112 / 30 chocolates per second = 56 / 15 chocolates per second. Boy's rate: 56 chocolates in 60 seconds. So his rate = 56 / 60 chocolates per second = 14 / 15 chocolates per second. Combined rate when both eat together = (56 / 15) + (14 / 15) = 70 / 15 chocolates per second. Simplify 70 / 15 = 14 / 3 chocolates per second. Time interval = 12 seconds. Total chocolates eaten together = (14 / 3) * 12 = 14 * 4 = 56. Hence, they can eat 56 chocolates together in 12 seconds.

Verification / Alternative check:
Check reasonableness: The girl is much faster than the boy. In 12 seconds the girl alone would eat (56 / 15) * 12 = 44.8 chocolates, while the boy would eat (14 / 15) * 12 = 11.2 chocolates. Their total is 44.8 + 11.2 = 56 chocolates, matching the combined rate calculation when we do not round intermediate values.

Why Other Options Are Wrong:
44 chocolates would be approximately the girl's contribution alone, ignoring the boy's help. 32 and 40 chocolates underestimate the total and do not respect the high rate of the girl. 49 chocolates is between the girl's solo contribution and the total, and does not match the precise sum of the two rates.

Common Pitfalls:
Some learners confuse half a minute with half an hour or do not convert seconds and minutes consistently. Others incorrectly average the chocolate counts instead of converting to per second rates. Always convert each person's performance into a rate in a common time unit, add the rates, and then multiply by the required time interval.

Final Answer:
The girl and her boyfriend can eat 56 chocolates together in 12 seconds.