Question

plz help me out with this

Answer 1

Let the time taken by the second cyclist to overtake the first one be n.
Distance travelled by the first cyclist = speed x time
                                                          = 11n  km
Distance travelled by the second cyclist 
                        in the first hour = 10km
                        second hour     = 10+1/3
                          and soo onn ......
Distance travelled by second cyclist = n/2{2(10)+(n-1)1/3}
                                                          =n/2{20+ 1n/3 -1/3}
                                                          =n/6{59+n}
                                                          =59n/6 + n^2/6
Distance travelled first cyclist = second cyclist
                                       11n   =59n/6  n^2/6
                                        66n  =n^2+59n
                                  n^2 - 7n = 0
                               n(n-7)       =0
                                             n =7

Therefore time taken by the second cyclist to overtake the first cyclist is 7 hours.