The child runs with speed vc.
The adult runs with speed va.
The adult gives the child a head start of distance d.
The speed can be calculated according the relationship between distance and time: speed=distance/time
In our case we are interested in the time ( how long will it take for the adult to catch the child)=> time=d/v
Let tc denotes the time of the child and ta of the adult.
tc=D/vc, where D=D+d , D+d=tc*vc, D=tc*vc-d
ta=D/va D=ta*va
tc*vc-d=ta*va
ta=tc*vc-d/va
