Alok starts walking from P with speed of 6 km/h towards Q. Raman starts at the same time from P towards Q with the speed of 9 km/h. Raman reaches Q, turns back, and starts walking towards P. He meets Alok at R. If PQ is 15 km, then what is PR ?

Alok starts walking from P with speed of 6 km/h towards Q. Raman starts at the same time from P towards Q with speed of 9 km/h.

PQ = 15 km

Raman can reach on point Q = $$\frac{15}{9}$$ = $$\frac{5}{3}$$ = 1 hour and 40 minutes.

In 1 hour and 40 minutes, Alok can cover distance from P = $$6\times{\frac{5}{3}}$$ = 10 km

Raman reaches Q, turns back and starts walking towards P.

Now 5 km distance is between Raman and Alok.

Time taken by both of them to cover the 5 km distance = $$\frac{5}{\left(9+6\right)}$$ = $$\frac{5}{15}$$ hours = 20 minutes.

Distance covered by Alok in 20 minutes = $$6\times\frac{5}{15}$$ = 2 km. So the remaining distance which is (5-2) =  3 km will be covered by Raman to meet each other.

So PR = distance covered by the alok = 10+2 = 12 km.