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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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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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 boy can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is ?

A) 1.8 kmph B) 2 kmph
C) 2.2 kmph D) 1.5 kmph
 
Answer & Explanation Answer: D) 1.5 kmph

Explanation:

Speed of Boy is B = 4.5 kmph

Let the speed of the stream is S = x kmph

Then speed in Down Stream = 4.5 + x

speed in Up Stream = 4.5 - x

As the distance is same,

=> 4.5 + x = (4.5 - x)2

=> 4.5 + x = 9 -2x

3x = 4.5

x = 1.5 kmph

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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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7 1863
Q:

A boatman can row 96 km downstream in 8 hr. If the speed of the current is 4 km/hr, then find in what time he will be able to cover 8 km upstream ?

A) 1.5 hrs B) 1 hrs
C) 2.5 hrs D) 2 hrs
 
Answer & Explanation Answer: D) 2 hrs

Explanation:

Speed in downstream = 96/8 = 12 kmph

Speed of current = 4 km/hr

Speed of the boatman in still water = 12 – 4 = 8 kmph

Speed in upstream = 8 – 4 = 4 kmph

Time taken to cover 8 km upstream = 8/4 = 2 hours.

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