A boat makes a journey from point P to point Q and return back in 6 hr 40 min. One way it travels with the stream and on the return it travel against the stream. Prdouct of speed in downstream and upstream is 216. If the speed of the stream increase by 2 km/hr, the return journey takes 7 hr 12 min. What is the speed of the boat in still water? The distance between P and Q is 48 km.

Solution

Let the speed of boat in upstream = x km/hr Speed of boat in downstream = y km/hr Condition I: 48/x + 48/y = 20/3 ………..(1) Condition II: 48/(x – 2) + 48/(y + 2) = 36/5 ………..(2) Solving these equations: 48x + 48y = 20xy/3 …………(1) 48x + 48y = 36(x – 2)(y + 2)/3 …………(2) 100xy = 108(x – 2)(y + 2)………(3) Product of speed boat in downstream and upstream = 216 xy = 216 ……(4) 100 x 216 = 108 (x – 2)(y + 2) 200 = 216 + 2x – 2y + 4 x – y = 6 …….(5) From eq(4) and (5), we got 216/y – y = 6 216 – y²= 6y y²+ 6y – 216 = 0 (y + 18)(y – 12) = 0 Hence, y = 12 and x = 12 + 6 = 18 Speed of boat in still water = 1/2 (18 + 12) = 15 km/hr