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.

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