Question

why does the rate of breathing increase while walking uphill at a normal place in the mountains?

Answer 1

because in that layer of atmosphere oxygen found is less so our lungs extract more o2 thrfore our breathing goes up

Answer 2

it is as because 1. the rate of breathing increases because higher we go lesser the oxygen we get, so as our breathing rate increases our body tries to intake more oxygen to fulfill the demand of oxygen in our body.
2. we walk against gravity as we climb uphill hence our body requires more energy and energy in our body is supplied by breaking down of oxygen molecules hence, to supply  more oxygen to our body our breathing rate increases.