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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. 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. 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

1. A boat covers a certain distance downstream in 1 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. 12 kmph
• B. 13 kmph
• C. 14 kmph
• D. 15 kmph
 Ans: D. Sol. Let the speed of the boat in still water be x kmph. Then, Speed downstream = (x + 3) kmph, Speed upstream = (x - 3)kmph. ∴ (x + 3) * 1 = (x -3) * 3/2 ⇔ 2x + 6 = 3x - 9 ⇔ x = 15 kmph.

2. A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a plce and come back, how far is the place?

• A. 2 km
• B. 2.4 km
• C. 2.5 km
• D. 3.4 km
 Ans: B. Sol. Speed downstream = (5+1) kmph = 6 kmph; Speed upstream = (5 - 1)kmph = 4 kmph. Let the required distance be x km. Then, x/6 + x/4 = 1 ⇔ 2x + 3x = 12 ⇔ 5x = 12 ⇔ x = 2.4 km.

3. The speed of a boat in still water is 15 km/hr and the rate of current is 3 km/hr the distance travelled downstream in 12 minutes is :

• A. 2 km
• B. 2.6 km
• C. 3.6 km
• D. 4 km
 Ans: C. Sol. Speed downstream = (15 + 3) kmph = 18 kmph. Distance travelled = [18 * 12/60] km = 3.6 km.