Boats and Streams


  1. The current of a stream runs at the rate of 4 km/hr. A boat goes 6 km and back to the starting point in 2 hours. The speed of the boat in still water is ?









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    Let the speed in still water be x km/hr
    Then, 6/x + 4 + 6/x - 4 = 2

    Correct Option: C

    Let the speed in still water be x km/hr
    Then, 6/x + 4 + 6/x - 4 = 2
    ⇒ 6[ x - 4 + x + 4] = 2(x2 - 16)
    ⇒ x2 - 6x - 16 = 0
    ⇒ (x - 8) (x + 2) = 0
    ∴ x = 8 km/hr


  1. A boat moves upstream at the rate of 1 km in 10 minutes and downstream at the rate of 1 km in 6 minutes. The speed of the current is ?









  1. View Hint View Answer Discuss in Forum

    Speed upstream = 6 km/hr
    Speed downstream = 10 km/hr
    ∴ Speed of the current = (10 - 6)/2 km/hr = 2 km/hr

    Correct Option: C

    Speed upstream = 6 km/hr
    Speed downstream = 10 km/hr
    ∴ Speed of the current = (10 - 6)/2 km/hr = 2 km/hr



  1. A man rows upstream 16 km and downstream 28 km talking 5 hours each time. The velocity of the current is ?









  1. View Hint View Answer Discuss in Forum

    Speed downstream = (28/5) km/hr = 5.6 km/hr
    Speed upstream = (16/5) km/hr = 3.2 km/hr

    Correct Option: B

    Speed downstream = (28/5) km/hr = 5.6 km/hr
    Speed upstream = (16/5) km/hr = 3.2 km/hr
    Velocity of current = (5.6 - 3.2)/2 km/hr = 1.2 km/hr


  1. A man can row at 5 km/hr in still water and the velocity of current is 1 km/hr. It takes him 1 hour to row to a place and back. How far is the place ?









  1. View Hint View Answer Discuss in Forum

    Speed downstream = (5 + 1) km/hr = 6 km/hr
    Speed upstream = (5 - 1) km/hr = 4 km/hr
    Let the required distance be d km
    Then, d/6 + d/4 = 1

    Correct Option: B

    Speed downstream = (5 + 1) km/hr = 6 km/hr
    Speed upstream = (5 - 1) km/hr = 4 km/hr
    Let the required distance be d km
    Then, d/6 + d/4 = 1
    ⇒ 2d + 3d = 12
    ∴ d = 2.4 km



  1. A man can row 44 km downstream in 4 hours. If the man's rowing rate in still water is 8 km/hr, then find in what time will he cover 25 km upstream ?









  1. View Hint View Answer Discuss in Forum

    Man's rate in still water = (man's rate with current + his rate against current)/2

    Correct Option: A

    ∵ Man's rate in still water = (man's rate with current + his rate against current)/2
    ⇒ 8 = 1/2 [ 44/4 + 25/T ]
    ⇒ 16 = 11 + 25/T
    ∴ T = 5 hours