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BOATS AND STREAMS

Aptitude

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

4. 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 the stream is:
 
  • A. 1:2
  • B. 1:3
  • C. 2:1
  • D. 3:1
Ans: D.
Sol.
Let man’s rate upstream be x kmph. Then, his rate downstream = 2x kmph.
∴ (Speed in still water) : (Speed of stream)
= [2x + x / 2] : [2x - x / 2]
3x / 2 : x / 2 = 3:1.
 
5. 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. 30 minutes
  • B. 45 minutes
  • C. 1 hour
  • D. 1 hour 15 min
Ans: D.
Sol.
Rate downstream = [16/2] kmph = 8 kmph; Rate upstream = [16/4] kmph = 4 kmph.
∴ Speed in still water = 1/2(8+4) kmph = 6 kmph.
 
 
6. A man rows to a place 48 km distance and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
 
  • A. 1 km/hr
  • B. 2.5 km/hr
  • C. 3 km/hr
  • D. 4 km/hr
Ans: A.
Sol.
Suppose he moves 4 km downstream in x hours. Then,
Speed downstream = [4/x] km/hr, Speed upstream = [3/x] km/hr.
∴ 48/(4+x) + 48/(3/x) = 14 or x = 1/2.
So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream = 1/2 (8-6) km/hr = 1 km/hr.