Reptiles, Mammals etc. can eat and breathe at the same time due to negative pressure brething.
Breathing requires pressure gradient to be created. Mammals and reptiles create this gradient in the lungs by using their diaphragms. This creates a high volume, low pressure in the lung cavity causing air to be sucked in. This eliminates the need of gulping air through the mouth as in frogs. Hence they can swallow food and breathe at the same time.