Let f and g be two continuous functions on the closed interval [0,1] such that for every x in [0,1] : f(x)<g(x).

Prove that there exists some number m>0 such that for every x in [0,1] : f(x)+m<g(x).

Well i think i have to use the fact that every continuous function on a closed interval is bounded by a maximum and a minimum, but since I've never dealt with anything like this I can't really start it. Thanks for the help before hand.