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BOATS AND STREAMS

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BOATS AND STREAMS -> IMPORTANT FACTS AND FORMULAE

I. In water, the direction along the stream is called downstream. And, the direction against the stream is called upstream.
II. If the speed of a boat in still water is u km/ht and the speed of the stream is v km/hr, then :
Speed downstream = (u + v) km/hr
Speed upstream (u - v) km/hr.
III. If the speed downstream is a km/hr and the speed upstream is b km/hr, then :
Speed in strill water = 1/2 (a + b) km/hr
Rate of stream = 1/2 (a - b) km/hr

BOATS AND STREAMS -> SOLVED EXAMPLES

1. In a stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water.
  Sol. Let the speed of the motorboat in still water be x kmph. Then,
Speed downstream = (x + 2) kmph; Speed upstream = (x - 2) kmph.
∴ 6/x+2 + 6/x-2 = 33/60
⇔ 11x² - 240x - 44 = 0
⇔ 11x² - 242x + 2x - 44 = 0
⇔ (x - 22) (11x + 2) = 0 ⇔ x = 22.
Hence, speed of motorboat in strill water = 22 kmph.
2. A man can row 18 kmph in still water. It takes him trice as long to row up as to row down the river. Find the rate of stream.
  Sol. Let man’s rate upsream be x kmph. Then, his rate downstream = 3x kmph.
∴ Rate in still water = 1/2(3x + x) kmph = 2x kmph.
So, 2x = 18 or x = 9.
∴ Rate upstream = 9 km/hr, Rate downstream = 27 km/hr.
Hence, rate of stream = 1/2(27 - 9) km/hr = 9 km/hr.
3. 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.
  Sol. 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.

BOATS AND STREAMS -> EXERCISE

10. In one hour, a boat goes 11 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is:
 
  • A. 2
  • B. 4
  • C. 8
  • D. 12
Ans: C.
Sol.
Speed in still water = 1/2 (11+5) kmph = 8 kmph.
 
11. A man rows downstream 32 km and 14 km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is:
 
  • A. 1.5 kmph
  • B. 1.75 kmph
  • C. 2 kmph
  • D. 3 kmph
Ans: A.
Sol.
Rate downstream = [32/6] kmph; Rate upstream = [14/6] kmph.
∴ Velocity of current = 1/2[32/6 - 14/6] kmph = 3/2 kmph = 1.5 kmph.
 
 
12. The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is:
 
  • A. 1 km/hr
  • B. 1.5 km/hr
  • C. 2 km/hr
  • D. 3 km/hr
Ans: D.
Sol.
Let the speed of the stream be x km/hr. Then,
Speed downstream = (10+x) km/hr, Speed upstream = (10 - x) km/hr.
∴ 26/(10+x) = 14/(10-x) ⇔ 260 - 26x = 140 + 14x ⇔; 40x = 120
x = 3 km/hr.