The time taken by a boat to travel a certain distance downstream is in the ratio 4:5 compared to the time taken to travel the same distance upstream. Additionally, the speed of the stream is reduced by 50% during the upstream journey. If the speed of the boat in still water is 13 m/s, determine the distance the boat covers downstream in 24 seconds.

ATQ, Let the speed of the stream while going downstream = ‘2a’ m/s So, the speed of the stream while the boat is going upstream = 50% of ‘2a’ = ‘y’ m/s Since the ratio of time taken by the boat to go a certain downstream distance to that taken to come back is 4: 5. So, the ratio of downstream speed to the upstream speed of the boat = 5: 4 (13 + 2a)/(13 – a) = 5/4 52 + 8a = 65 – 5a a = 1 Speed of stream while boat is going downstream = 2 × 1 = 2 m/s Downstream speed of the boat = 13 + 2 = 15 m/s So, downstream distance covered by the boat in 24 seconds = 15 × 24 = 360 m