A boat takes 8 hours to travel 42 km upstream and 81 km downstream combined. In another instance, it covers 48 km upstream and 54 km downstream in 7 hours. Determine the time the boat would need to travel 90 km in still water.

Solution

Let the upstream and downstream speeds of the boat are x km/h and y km/h. So according to question: 42/x + 81/y = 8 And, 48/x + 54/y = 7 Let 1/x = a and 1/y = b So 42a + 81b = 8 ………. (i) And 48a + 54b = 7 …….. (ii) Solving (i) and (ii) we get a = 1/12 and b = 1/18 So x = 12 and y = 18 So the upstream and downstream speeds of the boat are 12 km/h and 18 km/h respectively. So the speed of the boat in still water = (12 + 18)/2 = 15 km/h So the time taken by the boat to cover 90 km in still water = 90/15 = 6 hours