Non-monetary intergenerational transfers of time, such as informal care time transfers, represent a largely unknown, yet pivotal component of the support system in a country. In this article, we offer estimates of time transfers, by age and sex, related to informal childcare and adult care in the United States. We developed methods to extract both intra-household and inter-household time transfers from the American Time Use Survey (2011-2013) and the recently-added Eldercare Roster. We then summarized the results in matrices of time flows by age and sex for the general U.S. population, as well as for the so-called "sandwich generation." We observed that most time transfers flow downwards from parents to young children. Grandmothers spend more time with newborn grandchildren than grandfathers, who, on the other hand, spend more time with slightly older grandchildren. The time produced by the sandwich generation is directed towards a more diverse population spectrum, including substantial intra-generational transfers to spouses. Estimates of time produced and consumed by the population with various demographic characteristics establish a foundation for extrapolating the degree to which the demand for care services will be met in the years to come. Extrapolation based on our findings reveals a steady rise in demand, relative to supply, of informal care lasting decades into the future. This projection indicates that, to maintain current levels of care, our society will have to either rely more heavily on the market or on an increased effort of caregivers.