A man rows a boat at a speed of 15 mph in still water. Find the speed of the river if it takes her 4 hours 30 minutes to row a boat to a place 30 miles away and return



A man rows a boat at a speed of 15 mph in still water. Find the speed of the river if it takes her 4 hours 30 minutes to row a boat to a place 30 miles away and return.

A. 5 mph

B. 10 mph

C. 12 mph

D. 20 mph

Answer : A. 5 mph


Explanation:

    Let us assume that the speed of the river = x mph
    Speed of boat on outward journey = (15 – x) mph (Assuming the outward journey is upwards)
    Speed on boat on return journey = (15 + x) mph (Assuming the return journey is downwards)
    Time = Distance/Speed
    4 hours 30 minutes = 4.5 hours
    Total time taken = 30 / (15 – x) + 30 / (15 + x) = 4.5
    30(15 + x) + 30(15 - x) / (15 – x) (15 + x) = 4.5
    450 + 30x + 450 – 30x = 4.5 (225 – x2)
    900 = 4.5 (225 – x2)
    200 = 225 – x2
    x2 = 25
    x = 5
    The speed of river is 5mph.


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