Question

A starts at 11:00AM and travels at a speed  of 4km/hr. B starts at 1:00PM and travels at
1km/hr for the first 1hr and 2km/hr for the next hr and so on. At what time
they will meet each other.  

Answer 1

Let them meet at N hours in P. M. Obviously, T is after 1 PM.  We assume that A and B are traveling in the same direction and they start at the same point.

Distance traveled by A by time N hours = 4  * (N+1)  km
Distance traveled by B by time N hours = 1 km + 2 km + ... + (N-1) km
         So  4 N + 4 = (N-1) N /2
               8 N + 8 = N² - N
         N² - 9 N - 8 = 0  

         Δ = 81 + 32 = 113
         N = [9 +- √113 ]/2  =  9.815 hours PM
                 that is  9 PM and 48 minutes 54.26 sec