The monetary cost of running is about $100/year, biking considerably less. As for the cost in time, the average person in the bottom 25% of earnings spends 30 minutes/day more watching TV than the average person in the top 25% (2 hours, 6 minutes total). (No breakdown for "poverty" vs "non-poverty" is given.)
I think the poor could manage some exercise or preparation of healthier food if they wanted to.