Boats and Streams Questions

Q:

A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:

A) 1.8h B) 3h
C) 4h D) 5h
 
Answer & Explanation Answer: B) 3h

Explanation:

Upstream speed = B-S

Downstream speed = B+s

B-S = 15/5 = 3 km/h

Again          B= 4S

Therefore    B-S = 3= 3S

=>             S = 1 and B= 4 km/h

Therefore    B+S = 5km/h

Therefore, Time during downstream = 15/5 = 3h

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Q:

A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the rate of stream of the river ?

Answer

\inline \frac{Time\: taken\: in\: upstream}{Time\: taken\: in\: downstream} = \inline \frac{2}{1}


 \inline \therefore \inline \frac{Downstream\: speed}{upstream\: speed} = \inline \frac{2}{1}        where  \inline \frac{B+R}{B-R}=\frac{2}{1}


B ---> speed of boat in still water


R---->speed of current


\inline \Rightarrow \frac{B}{R}=\frac{3}{1}    ( By componendo and dividendo)


\inline \Rightarrow \frac{9}{R}=\frac{3}{1}\: \: \Rightarrow R= 3\: km/h

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38 5516
Q:

A man goes down stream with a boat to some destination and returns upstream to his original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and 14km/hr respectively, the distance of the destination from the string place is 

A) 16 km B) 18 km
C) 21 km D) 25 km
 
Answer & Explanation Answer: C) 21 km

Explanation:

Let the distance covered be D km. 

 D10+4+ D10-4 = 5

 D14+D6=5

 10D = 42 x 5 = 210

 

=> D = 21 km

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Q:

A motor boat takes 12 hours to go downstream and it takes 24 hours to return  the same distance. what is the time taken by  boat in still water?

A) 15 h B) 16 h
C) 8 h D) 20 h
 
Answer & Explanation Answer: B) 16 h

Explanation:

If t1 and t2 are the upstream and down stream times. Then time taken in still water is given by 

2×t1×t2t1+t2=2×12×2436=16h

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12 3323
Q:

The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?

A) 8 kmph B) 6 kmph
C) 7.5 kmph D) 5.5 kmph
 
Answer & Explanation Answer: B) 6 kmph

Explanation:

Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph

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8 3309
Q:

A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at 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) 160 km
C) 140 km D) 120 km
 
Answer & Explanation Answer: A) 180 km

Explanation:

Speed in downstream = (14 + 4) km/hr = 18 km/hr;

Speed in 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.

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Q:

A man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time. Find the speed of the stream ?

A) 5 kmph B) 10 kmph
C) 15 kmph D) 45 kmph
 
Answer & Explanation Answer: A) 5 kmph

Explanation:

Speed of the boat downstream  s=a/t= 60/3 = 20 kmph

Speed of the boat upstream s= d/t = 30/3= 10 kmph

 

Therefore,  The speed of the stream = speed of downstream - speed of upstream2=5 kmph

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Q:

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?

A) 4.58 kms B) 6.35 kms
C) 5.76 kms D) 5.24 kms
 
Answer & Explanation Answer: C) 5.76 kms

Explanation:

Speed in still water = 6 kmph

Stream speed = 1.2 kmph

Down stream  = 7.2 kmph

Up Stream = 4.8 kmph

x/7.2 + x/4.8 = 1

x = 2.88

Total Distance  = 2.88 x 2 = 5.76 kms

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