# the distance covered by sodier

Let v1 be the speed of last soldier

&

v2 be the speed of the marching troop

So relative velocity of soldier in forward motion is v1-v2

&

relative vel. in backward motion is v1+v2

=> time(t) = distance / velocity

So, 150/v2 = 80/(v1-v2) + 80/(v1+v2) = time(t)

=> v2= 150/t

=> putting v2= 150/ t in the above equation we get,

=> v1t^2 -160v1t – 22500=0

=> v1t^2 -250v1t + 90v1t -22500=0

=> (v1t -250)(v1t +90)=0

Now we get ,Distance covered by soldier = v1 * t = 250m