Time speed and distance - And so we meet again...

Question :-
A pedestrian and a cyclist left nagpur to buti bori at the same time.Having reached buti bori, the cyclist turned back and met the pedestrian an hour after the start.After their meeting,the pedestrian continued his trip to buti bori and the cyclist turned back and also head to buti bori.Having reached buti bori, the cyclist turned back again and met the pedestrian 30 mins after their first meeting.Determine what time it takes the pedestrian to cover distance between nagpur and buti bori.



Solution :- Let the speed of the pedestrian and cyclist be p and c resp. Let the distance between the two stations be x we need to find x/p

Now, When they meet for the first time, total distance covered by both pedestrian and car together will be 2x as shown in figure above.
=> p+c=2x ....eq1 (Remember This)

Using same concept, in the nxt 30 mins the scenario will be 2(x-p)=c/2+p/2 (30min is half hour, so distance covered will be half of speed.)
=> 4(x-p)=p+c ....eq2

Using eq1 and eq2 we can find out x/p which is the time required for pedestrian.
=> x/p= 2 hours