A boat travels 20 kms upstream in 6 hrs and 18 kms downstream in 4 hrs.Find the speed of the boat in still water and the speed of the water current?
(a) 1/2 kmph (b) 7/12 kmph (c) 5 kmph (d) none of these

• Speed of boat upstream = 20/6 km
  Speed of boat downstream = 18/4 km = 9/2 km = 27/6 km
  
  Now, the current is helping the boat down stream. This makes their speed combine. For upstream, it is basically the speed of the boat minus the speed of the river if you think about it. This results in:
  
  { x + y = 27/6
  { x - y = 20/6
  
  Adding these gives us:
  
  x + y = 27/6
  x - y = 20/6
  ------------------
  2x = 47/6
  x = 47/12
  
  Plugging this into the top equation gives:
  
  x + y = 27/6
  ==> 47/12 + y = 54/12
  ==> y = 7/12
  
  Therefore, the boat's speed is 47/12 km ≈ 3.92km and the current's speed is 7/12 km ≈ 0.58km.
  
  Hope this helps!
• 12 years agoHelpfull: Yes(27) No(8)
• upstream velocity =20/6
  downstream =18/4
  speed of stream = (downstream speed -upstream speed)/2
  =7/12
• 11 years agoHelpfull: Yes(9) No(2)
• let the speeed of the boat is U
  and speed of the water is V
  upstream= V-U
  down Stram= V+U
  there fore from problem V-U=20/6 -------1
  V+U=18/4-------------2
  solve 1 and 2
  we get v=47/12,U=7/12
• 6 years agoHelpfull: Yes(0) No(0)
• Speed of boat upstream = 20/6 km
  Speed of boat downstream = 18/4 km = 9/2 km = 27/6 km
  
  Now, the current is helping the boat down stream. This makes their speed combine. For upstream, it is basically the speed of the boat minus the speed of the river if you think about it. This results in:
  
  { x + y = 27/6
  { x - y = 20/6
  
  Adding these gives us:
  
  x + y = 27/6
  x - y = 20/6
  ------------------
  2x = 47/6
  x = 47/12
  
  Plugging this into the top equation gives:
  
  x + y = 27/6
  ==> 47/12 + y = 54/12
  ==> y = 7/12
  
  Therefore, the boat's speed is 47/12 km ≈ 3.92km and the current's speed is 7/12 km.
• 6 years agoHelpfull: Yes(0) No(0)