This study explores how gender and race intersect to shape graduate students' experiences in academic workspaces using in-depth interviews with 67 biology PhD students. Building on recent intersectional research, our study highlights ways that race and gender create inequality in graduate education. Extending previous research on faculty, we highlight how gendered and racialized expectations that produce task differentiation emerge early in the academic career -- during graduate education. By considering the intersection between gender and race, we find not only do women biology graduate students do more service than men, but also racial and ethnic minority men do more service than do white men. White men benefit from a combination of racial and gender privilege, which places them in the most advantaged position with respect to protected research time and opportunities to build collaborations and networks beyond their labs. Racial/ethnic minority women emerge as uniquely disadvantaged in terms of their experiences relative to other groups. These findings illuminate how gender and racial inequality regimes combine to shape students' experiences in biology laboratories. Moreover, they expand Acker's concept of gendered organizations to include race and specify how distinct gender-race groups experience academic workplaces.