A user provides a language model with the following word problem: 'A factory has 5 machines that can make 5 widgets in 5 minutes. At this rate, how long would it take 100 machines to make 100 widgets?'

Below are two different responses generated by the model based on two different prompting approaches:

Response A: 'It would take 100 minutes for 100 machines to make 100 widgets.'

Response B: 'Let's break this down. If 5 machines make 5 widgets in 5 minutes, this means each machine takes 5 minutes to make 1 widget. The machines work in parallel. Therefore, if you have 100 machines, each machine will still take 5 minutes to make its own widget. Since they all work at the same time, it will take 5 minutes to make 100 widgets.'

Analyze the two responses. Explain why Response B arrives at the correct answer while Response A does not, focusing specifically on the differences in the problem-solving process demonstrated in each output.