Final answer:
During headward erosion, the stream lengthens as it erodes the landscape at its headwaters, therefore the distance from the mouth to the source of the stream increases. The correct option is b.
Step-by-step explanation:
During the process of headward erosion, which is a form of river or stream erosion, the length of a stream increases over time as the stream cuts into the land. As the river or stream flows away from the source, typically, several geomorphological processes widen the channel, the current slows, and there may be increased sedimentation.
However, headward erosion works at the source of the river or stream, effectively lengthening the stream as it erodes the landscape at its headwaters. This means that the distance from the mouth to the source of the stream increases. The phenomenon of increasing stream length can also lead to the river or stream capturing or 'pirating' another stream's flow, which occurs when a stream or river extends its reach into another stream's watershed.
Hence, Option b is correct.