Hey

Vr=3.8km/h

Vb=11.4km/h

L=5.1km

Velocity=distance/time

time b reach finish:

vb=d/t

11.4=5.1/t

t = 0.44737hr*60mins

=26.8421mins

d=vr*t R distance in that time

=3.8*0.44737

=1.7km

distance left

5.1km - 1.7km =3.4km

Find the time that the runner and bird meet:

You know the total distance and both there distances should add to that total

3.4 = distB + distR (substitute d=v*t)

3.4 = (vb*t)+(vr*t)

3.4 = (11.4*t)+(3.8*t) solve for t

3.4 = 15.2t

t = 0.2237hrs *60min

= 13.4210mins

Total B dist:

dtotal = (.44737*11.4)+(.2237*11.4)

= 7.65km

Therefore the bird traveled a total of 7.65km