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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

7. A man can row 9 1/3 kmph in still water and finds that it takes him thrice as uch time to row up than as to row down the same distance in the river. The speed of the current is:
 
  • A. 3 1/2 km/hr
  • B. 2 1/3 km/hr
  • C. 4 1/2 km/hr
  • D. 4 2/3 km/hr
Ans: D.
Sol.
Let speed upstream be x kmph. Then, speed downstream = 3x kmph.
Speed in still water = 1/2(3x + x) kmph = 2x kmph.
∴ 2x = 28/3 ⇒ x = 14/3
So, Speed upstream = 14/3 km/hr; Speed downstream = 14/hr.
Hence, speed of the current = 1/2 [14 - 14/3] km/hr = 14/3 km/hr = 4 2/3 km/hr.
 
8. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
 
  • A. 12 hours
  • B. 24 hours
  • C. 36 hours
  • D. 48 hours
Ans: B.
Sol.
Speed upstream = 7.5 kmph; Speed downstream = 10.5 kmph.
∴ total time taken = [105/7.5 + 105/10.5] hours = 24 hours.
 
 
9. A boat takes 19 hours for travelling downstream fro poin A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B?
 
  • A. 180 km
  • B. 190 km
  • C. 220 km
  • D. 230 km
Ans: A.
Sol.
Speed downstream = (14 + 4) km/hr = 18 km/hr;
Speed upstream = (14 - 4) km/hr = 10 km/hr.
Let the distance between A and B be x km. Then,
x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km.