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Problems on Boats and Streams

Important Formulas:


  1. If the speed of a boat in still water be x km/hr and that of stream be y km/hr
    a) Speed of the boat downstream = (x+y) km/hr
    b) Speed of the boat upstream = (x-y) km/hr

  2. If the speed of a boat downstream is u km/hr and speed upstream is v km/hr
    a) Speed of the boat in still water = 1/2(u + v) km/hr
    b) Speed of the current =1/2(u - v) km/hr

  3. If a man rows in still water at x km/hr and the rate of current (or stream) is y km/hr
    a) Man's rate with the current = (x+y)km/hr
    b) Man's rate against the current = (x-y)km/hr


  1. A man can row upstreams at 6 km/hr and down streams at 11 km/hr. Find man's rate in still water and the rate of the current?
    Ans: Rate in still water=1/2(6 + 11) = 8.5 km/hr.
    Rate of current =1/2(11 - 6)= 2.5 km/hr.

  2. A man can row 9 km/hr in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream.
    Ans: Let man's rate in upstream = x km/hr.
    man's rate downstream = 2x km/hr.
    Therefore Man's rate in still water = 1/2(x+2x)km/hr.
    ie, 3x/2 = 6 ⇒ x=4.
    Therefore Rate upstream = 4 km/hr.
    & Rate downstream = 8 km/hr.
    Rate of current = 1/2(8-4) km/hr.
    = 2 km/hr.

  3. A boatman can row 3 km against the stream in 45 minutes and return in 30 minutes. Find the rate of his rowing in still water and also the speed of the stream?
    Ans: Let the speed of the boatman in still water be x km/hr and the speed of the stream be y km/hr.
    Time taken to row against the stream = 45/60 = 3/4 hr.
    Time taken to row with the stream = 30/60 = 1/2 hr.
    Speed against current = x-y = Distance/Time = 3/3/4 = 4 km/hr.
    Speed with current = x+y = Distance/Time = 3/1/2 = 6 km/hr.
    Therefore x+y = 6 & x-y = 4
    ⇒ x=5 km/hr & y = 1 km/hr

Practise Test:

  1. A boat takes 9 hrs to travel from A to B upstream. If the river current is 3 km/hr, how long will it take to travel downstream between B and A?
    1) 3 hrs   2) 6 hrs   3) 4.5 hrs   4) 5 hrs

  2. A boat goes 11 km in an hour with the stream and 5 km in an hour against the stream. The speed of the boat (in km/hr.) in still water is
    1) 5   2) 6   3) 8   4) 9

  3. A man rows upstream 13 km and down stream 28 km taking 5 hrs each time. The velocity of the current in km/hr. is
    1) 0. 5   2) 1   3) 1. 5   4) 2

  4. A boat moves down stream at the rate of 1 km in 7.5 mts and upstream at the rate of 5 km/hr. The speed of the boat (in km/hr.) in still water is
    1) 6   2) 6. 5   3) 7   4) 7. 5
  5. A boat can be rowed 9 km upstream or 18 km downstream in a period of 3 hrs. What is the speed of the boat in still water in kmph?
    1) 1. 5   2) 3   3) 4. 5   4) 6

  6. A boatman can row to a place 48 km distant and back, in 14 hrs. If he can row 4 km with the stream in the same time as 3 km against it, the speed of the stream (in km/hr) is
    1) 1   2) 2.2   3) 3   4) 0. 5

Answers for practise test:

7 . (4) 8.(3) 9 . (3) 10. (2) 11. (3) 12. (1)

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