question_answer

  A boat covers 32 km upstream and 36 km downstream in 7 h. Also, it covers 40 km upstream and 48 km downstream in 9 h. Find the speed of the boat in still water and that of the stream.

Answer:

  Let the speed of the boat in still water be x km/h and that of the stream be  Then, Speed upstream  Speed downstream Now, time taken to cover 32 km upstream Time taken to cover 36 km downstreamThe total time of journey is 7 h.                                  ?(i)(1/2) Time taken to cover 40 km upstream Time taken to cover 48 km downstream In this case, total time of journey is 9 h.                                           ?(ii) Putting and in Eqs. (i) and (ii), we get                                          ?(iii) and                                                      ?(iv)(1/2) By cross-multiplication, in Eqs (iii) and (iv) we have                                        (1/2)                               and                        (1/2)                     We have,                                                                                               ?(v) and                                                                                             ?(vi)(1) On adding Eqs. (v) and (vi), we get                           On putting the value of in Eq. (vi), we get                                                           Hence, the speed of the boat = 10 km/h and the speed of the stream = 2 km/h          (1/2)