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karansingh
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Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

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  1. Given: Speed of boat in still water = 15 km/hr.

    Let the speed of stream = x km/hr.

     

    Distance covered by boat in going upstream = Distance covered by boat in downstream = 30 km

     

    Speed of boat upstream = Speed of boat in still water – Speed of stream = (15 – x) km/hr.

     

    Speed of boat downstream = Speed of boat in still water + Speed of stream = (15 + x) km/hr.

     

    Since, Distance = Speed × Time

     

    ⇒ Time = Distance / Speed

     

    Time taken by boat upstream = 

     

    Time taken by boat downstream 

     

    Total time taken by the boat to go and come back to the same point = 4.5 hrs.

     

    ∴ 

     

    Multiply and divide both sides by (15 – x)(15 + x):

     

    ⇒ 4.5 (225 – x2) = 30(15 + x) + 30(15 – x)

     

    ⇒ 1012.5 – 4.5x2 = 450 + 30x + 450 – 30 x

     

    ⇒ 1012.5 – 4.5x2 = 900

     

    ⇒ 4.5x2 = 112.5

     

    ⇒ x2 = 25

     

    ⇒ x =  5

     

    But speed can’t be negative, ∴ Speed of the stream = 5 km/hr.

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