Question
The combined speeds of boats 'P' and 'Q' in still water
amount to 52 km/hr. The current's speed affecting boat 'P' is 25% greater than that affecting boat 'Q'. Boat 'Q' can cover 1927 km downstream in 41 hours, while boat 'P' takes 47 hours to cover the same distance downstream. Determine the upstream speed of boat 'P'.Solution
ATQ, Speed of boat ‘P in still water be ‘p’ km/hr Therefore, speed of boat ‘Q’ in still water = (52 – p) km/hr Let the speed of the current for boat ‘Q’ be q km/hr Therefore, speed of current for boat ‘P’ = 1.25q km/hr According to the question, (p + 1.25q) = 1927/47 = 41 ….. (1) Also, (52 – p + q) = 1927/41 = 47 …. (2) On solving equation (1) and (2), we get Speed of boat ‘P’ in still water = p = 21 km/hr Speed of the current for boat ‘Q’ = q = 16 km/hr Therefore, speed of the current for boat ‘P’ = 1.25q = 20 km/hr Therefore upstream speed of boat ‘P’ = p – 1.25q = 21 – 20 = 1 km/hr
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