How come the breathing and pulse rate increases as the length of exercise increases?

More need for oxygen: Your breath rate increases because your body tissues are increasing their metabolism, increasing the co2 in your bloodstream. This will make your blood more acidic, triggering an response in your brainstem to exchange it for oxygen. Your hr increases because your body produces Epinephrine under stress, which causes the sa node to fire more rapidly. This feeds all that new oxygen to your muscles.

Cardiac drift: With prolonged exercise, breathing rate increases to meet the oxygen demands of working muscle. Heart rate increases, but it does not plateau. A steady increase in heart rate is seen with prolonged exercise due to 'cardiac drift'. The heart rate increases in order to maintain your cardiac output in the face of decreased 'preload' due to dehydration and blood diverting to skin for heat loss.