question_answer

Two straight roads \[{{R}_{1}}\] and \[{{R}_{2}}\] diverge from a point A at an angle of\[120{}^\circ \]. Nitin starts walking from point A along \[{{R}_{1}}\]at a uniform speed of 3 km/hr. Prakash starts walking at the same time from A along \[{{R}_{2}}\]at a uniform speed of 2 km/h. They continue walking for 4 hours along their respective roads and reach point B and C on \[{{R}_{1}}\]and \[{{R}_{2}},\] respectively. There is a straight line path connecting B and C. Then Nitin returns to point A after walking along the line segments BC and CA. Prakash also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Nitin's and Prakash's return to the point A is:

A)  \[\frac{10\sqrt{19+26}}{3}\]                

B)  \[\frac{2\sqrt{19}+10}{3}\]

C)  \[\frac{\sqrt{19}+26}{3}\]                    

D)  \[\frac{\sqrt{19}+10}{3}\]

E)  None of these