A train leaves Delhi at 10 a.m. and reaches Jaipur at 4 p.m. on same day. Another train leaves Jaipur at 12 p.m. and reaches Delhi at 5 p.m. on same day. What is the time of day (approximately) when the two trains will meet?
A train leaves Delhi at 10 a.m. and reaches Jaipur at 4 p.m. on same day. Another train leaves Jaipur at 12 p.m. and reaches Delhi at 5 p.m. on same day. What is the time of day (approximately) when the two trains will meet? Correct Answer 1 : 49 p.m.
Let the total distance between Delhi and Jaipur be a
Travel time of train A going from Delhi to Jaipur = 4 p.m – 10 a.m = 6 hours
⇒ Speed of train A = a/6 km/hr
Travel time of train B going from Jaipur to Delhi = 5 p.m – 12 p.m = 5 hours
⇒ Speed of train A = a/5 km/hr
⇒ Distance covered by train A in 2 hours = (a/6) x 2 = a/3
Distance left for train A to cover when time is 12 : 00 pm = a – a/3 = 2a/3
Relative velocity for train A w.r.t B = a/6 + a/5 = 11a/30
⇒ Time Taken = Distance/speed= (2a/3)/(11a/30) = 20/11 hours
∴ required time = 12 : 00 pm + 20/11 hours = 1 : 49 pm