Mentoring is a collaborative process that guides students so they understand their scientific goals. It creates a structured course of action enabling them to accomplish their objectives. For example, mentoring in science includes motivating one to perform research and not give up when research does not go as planned. Mentoring also involves helping students get through crises when they arise. After all, a happy student is a happy researcher!
As a faculty member in a diverse department, I do not feel obligated to mentor--I want to! It's our responsibility as educators to guide students. I enjoy being a mentor, and I've had high school students, undergraduates, and graduate students working in my group, both male and females--as well as minorities.
During my first year as a professor at Louisiana State University  (LSU), I was the only female tenure-track faculty member (LSU has since hired two others) in a diverse department, so I can easily identify with Professor Jones in the case study. Because they identify with me, I am especially popular with our female students. Although many students, both male and female, tend to seek advice from me, I don't feel that it interferes with my professional activities. I am still able to run my own lab, perform interdisciplinary research, and serve on faculty committees. I make it clear when I am available, which makes mentoring more manageable.
Many of the students whom I mentor are in my senior colleagues' groups, but I don't mind lending a helping hand. After all, the senior colleagues in our department mentor their junior faculty and want to see them succeed. They read my proposals and give me effective teaching advice, which also makes me more efficient. Mentoring their students is the least I can do. If we expect to see students excited about science, we as scientists have to be approachable and friendly. Making ourselves available can break down barriers.
I was quite fortunate to have a Ph.D. advisor who was an excellent mentor. She guided my research and was available for counseling when needed. As a faculty member, I now feel honored to have the opportunity to affect students.
As for underrepresented groups, faculty should be willing to mentor students if approached. If a student feels comfortable interacting with the professor and solicits advice, then the faculty member should provide assistance. In my first semester at LSU, I got to know quite well an African-American undergraduate student in my advanced inorganic class, and I proceeded to "plant scientific seeds." She is now considering graduate school. What a great experience that was!
After reflecting on my own experience, I think that Carol should mentor Sarah. After all, how much time will this require? As faculty members, we should guide students--especially those who identify with us. This actually can be a very encouraging act. If Carol feels that she is too busy, she can have Sarah return at a later time. Sarah should also consider approaching other faculty members. She should not feel able to approach only Carol because she is a woman. I suspect some of the male faculty members would also be available for advice, especially those who have active industrial contacts and collaborations. My advice to all the other Sarahs out there is not to be afraid to ask questions ... even of those who might be different from you.