Answer to Question #306555 in Differential Equations for Munif

Question

Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed.

Answer 1

Solution;

Let assume they start at the same time t=a;

So;

$g(a)=h(a)$

So that;

$f(a)=g(a)-h(a)=0$

The finish at the same time . Assume t=b;

$f(b)=g(b)-h(b)=0$

Hence ,there will be some point at time t=c,when speed is equal to zero .