Arithmatical -Boats and Streams

DIRECTIONS : Problems based on Boats and Streams.
6. A boat covers a certain distance downstream in I hour, while it comes back in 1½ hours. If the speed of the stream be 3 kmph. what is the speed of the boat in still Water?
  A.  12kmph
  B.  13kmph
  C.  15kmph
  D.  16kmph
Solution
Let the speed of the boat in still water be x kmph. Then,
Speed downsteram= (x + 3) kmph.
Speed upsteram= (x - 3) kmph.
= (x+3)x1
= (x - 3)x3/2 kmph.
= 2x+6 = 3x-9
x= 15 kmph.
7. A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr The man's speed against the current is
  A.  8.5 km/hr
  B.  9 km/hr
  C.  10 km/hr
  D.  12.5 km/hr
Solution
Man's rate in still water= (15 - 2.5) km/hr
= 12.5 km/hr.
Man's rate against the current= (12.5 - 2.5) km/hr
= 10 km/hr.

8. A man can row upstream at 7 kmph and downstream at 10 kmph.Find man's rate in still water and the rate of current?
  A.  1.2 km/hr
  B.  1.5 km/hr
  C.  1.6 km/hr
  D.  1.8 km/hr
Solution
Rate in still water= 1 / 2 (10 + 7) km/hr
= 8.5 km/hr.
Rate of current= 1 / 2(10 - 7) km/hr
= 1.5 km/hr.
9. A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
  A.  40 minutes
  B.  1 hour
  C.  1 hour 15 min
  D.  1 hour 30 min
Solution
Rate downstream= (1 / 10 x 60)km/hr
= 6 km / hr.
Rate upstream= 2 km/hr.
Speed in still water= 1 / 2(6 + 2)km/hr
= 4 km.
Required time = (5 / 4) km/hr
= 1x 1/4 km/hr
= 1 hr 15 min.
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