Boats and Streams Problems and Solutions

• 8. A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.

  1. 4 hours
  2. 5 hours
  3. 6 hours
  4. 7 hours

  Answer :

  Option A

  Explanation:

  It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
  
  Lets see the question now.
  Speed downstream = (16 + 5) = 21 kmph
  
  Time = distance/speed = 84/21 = 4 hours

• 9. A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.

  1. 1 km/hr
  2. 2 km/hr
  3. 3 km/hr
  4. 4 km/hr

  Answer :

  Option A

  Explanation:

  First of all, we know that
  speed of current = 1/2(speed downstream - speed upstream) [important]
  
  So we need to calculate speed downstream and speed upstream first.
  
  Speed = Distance / Time [important]
  
  \begin{aligned}
  \text {Speed upstream =}\\ (\frac{15}{3\frac{3}{4}}) km/hr \\
  = 15 \times \frac{4}{15} = 4 km/hr \\
  
  \text{Speed Downstream = }
  (\frac{5}{2\frac{1}{2}}) km/hr \\
  = 5 \times \frac{2}{5} = 2 km/hr \\
  \text {So speed of current = } \frac{1}{2}(4-2) \\
  = 1 km/hr
  \end{aligned}

• 10. If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is

  1. 12 kmph
  2. 13 kmph
  3. 14 kmph
  4. 15 kmph

  Answer :

  Option B

  Explanation:

  Rate upstream = (7/42)*60 kmh = 10 kmph.
  Speed of stream = 3 kmph.
  Let speed in sttil water is x km/hr
  Then, speed upstream = (x —3) km/hr.
  x-3 = 10 or x = 13 kmph

• 11. A man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes. His rowing speed in still water is

  1. 4 kmph
  2. 5 kmph
  3. 6 kmph
  4. 7 kmph

  Answer :

  Option B

  Explanation:

  Rate upstream = (750/675) = 10/9 m/sec
  Rate downstream (750/450) m/sec = 5/3 m/sec
  Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec.
  = 25/18 m/sec
  = (25/18)*(18/5) kmph
  = 5 kmph

• 12. A man can row upstream 10 kmph and downstream 20 kmph. Find the man rate in still water and rate of the stream.

  1. 0,5
  2. 5,5
  3. 15,5
  4. 10,5

  Answer :

  Option C

  Explanation:

  Please remember,
  If a is rate downstream and b is rate upstream
  Rate in still water = 1/2(a+b)
  Rate of current = 1/2(a-b)
  
  => Rate in still water = 1/2(20+10) = 15 kmph
  => Rate of current = 1/2(20-10) = 5 kmph

• 13. A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat in still water and stream is

  1. 3:1
  2. 1:3
  3. 2:4
  4. 4:2

  Answer :

  Option A

  Explanation:

  Let speed downstream = x kmph
  Then Speed upstream = 2x kmph
  
  So ratio will be,
  (2x+x)/2 : (2x-x)/2
  => 3x/2 : x/2 => 3:1