Mathematics · Relative Speed and Clock Coding

In a certain code language, the following symbols represent the time in a clock as follows: - '%' means either the hour hand or the minute hand is at 2 - '+' means either the hour hand or the minute hand is at 5 - '?' means either the hour hand or the minute hand is at 3 - ' ' means either the hour hand or the minute hand is at 12 - '~' means either the hour hand or the minute hand is at 8 Note: If two symbols are given, then by default, the first symbol represents the hour hand and the second one represents the minute hand; all times are considered in the PM. For example, <~ = 4:40 PM. Train D, traveling at a uniform speed of 10 m/s, leaves Agra for Lucknow at %<. Train F travels from Lucknow to Agra and starts its journey at %~. Train F travels one-third faster than train D. At what time would both trains meet each other if the distance between Agra and Lucknow is 138 km?