Together Noodles & Freckles eat 50-lbs of dog food in 30 days. Noodles by himself eats 50-lbs in two weeks less time than Freckles does by himself. How many days to the nearest whole day would a 50-lbs bag of dog food last Freckles?

Solution:

Freckles: x

Noodles: x-14

So

1/x + 1/(x-14) = 1/30

So

x = 68

So a 50-lbs bag of dog food last Freckles for 68 days