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
A child runs at speed vc while an adult runs at speed va. if the adult gives the child a head start of distance d, how long will it take for the adult to catch the child? express your answer in terms of va and vc and d.