Solving Statement For Upstream And Downstream


 
 
Concept Explanation
 

Solving Statement For Upstream And Downstream

In these type of situations, while calculating upstream speed we subtract the speed of river from the speed of boat because the river is pushing the boat downwards even when the boat is moving upwards. Whereas when the boat is moving downstream the speed is calculated by adding the speed of river to the speed of boat.

 

Let the speed of a boat ( or a body) in still water be x km/h and that of stream be y km/h, then

  • Speed of boat downstream = (x +y ) km/h
  • Speed of boat upstream = ( x - y) km/h
  • Let the speed of boat in downstream and upstream be u km/h and v km/h, then

    Speed of boat in still water

    =frac{1}{2}(u-v)km/h

    Illustration: A boat goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream is 1 km/hr. Calculate the speed of boat in still water.

    A. 15 Km/h          B. 7.5 Km/h          C. 19 Km/h           D. 7 Km/h

    Answer: C

    Solution:     Let the speed of boat in still water be x km/hr

    Speed of stream  = 1 km/hr

    Speed upstream = x - 1 km/hr

    Speed Downstream = x + 1 km/hr

    As we know

     large speed= frac{distance}{time}

    Rightarrow distance= speed; X ;time

    Distance upstream = (x-1) X 10 = 10x - 10 Km

    Distance Downstream = (x+1) X 9 = 9x + 9 Km

    According to the question the distance is the same

                              10x-10 = 9x + 9

                              10x - 9x = 9+ 10

                                        x = 19 km/hr

    So the speed of boat in still water = 19 km/h

    Hence the correct option is C.

    Illustration: A motor boat whose speed in still water is 15 km/h, goes 40 km down stream and comes back in a total time of 6 hours. Find the speed of stream.

    A. 5 Km/h          B. 6 Km/h          C. 15 Km/h           D. 7 Km/h

    Answer: A

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    Sample Questions
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    Question : 1

    A person can row 7frac{1}{2} km/h in still water. It takes him twice as long to row up a distance as to row down the same distance. Find the speed of the stream.

    Right Option : C
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    Question : 2

    A boat goes downstream from one point to another in 12 hours. It covers the same distance upstream in 15 hours. If the speed of the stream is 1 km/hr. Calculate the speed of boat in still water.

    Right Option : B
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    Explanation
    Question : 3

    The ship left the harbor and is travelling 60 kilometers downstream. Then it continues on the tributary river (upstream) 20 kilometers. Travel took 77 hours to finish. River speed is 11 km/h. Calculate the speed of a ship.

    Right Option : B
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