Question

A boat with its motor set to half maximum speed takes 12 hours to travel 210 km up a river and 7 hours to travel back. 4 hours and 90 km into the return journey a wind suddenly picks up and pushes the boat along. 1. Find the still water speed of the boat, the wind speed, and the speed of the current in the river. (3 marks) a.

Answer 1

Let the speed of boat in still water be 'x'. Let the speed of current in river be 'y'. Let the speed of wind be 'z'. Upstream journey: - (x - y) = 210/12 . . . . .(1) [as speed of boat and current in river are in opposite direction] According to the question, In downstream journey, For first four hours and 90 km, there is no wind therefore 90 = (x + y) times 4 . . . . . .(2) For second half, i.e., (210 - 90) km and 3 hrs, wind is there therefore 120 = (x + y + z) times 3 . . . . .(3) \r\n on solving (1) and (2) x = 20 km/hr y = 2.5 km/hr Putting these values in (3) implies 120 = (20 + 2.5 + 2) times 3 therefore 22.5 + z = 40 z = 17.5 km/hr therefore speed of wind is 17.5 km/hr