# 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

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

51 9858
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 ?

$\inline&space;\frac{Time\:&space;taken\:&space;in\:&space;upstream}{Time\:&space;taken\:&space;in\:&space;downstream}$ = $\inline&space;\frac{2}{1}$

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

B ---> speed of boat in still water

R---->speed of current

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

$\inline&space;\Rightarrow&space;\frac{9}{R}=\frac{3}{1}\:&space;\:&space;\Rightarrow&space;R=&space;3\:&space;km/h$

8728
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

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.

19 8059
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

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

18 7555
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

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

9 6274
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

Explanation:

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

$2×t1×t2t1+t2=2×12×2436=16h$

22 6273
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

Explanation:

Let the distance covered be D km.

$D14+D6=5$

10D = 42 x 5 = 210

=> D = 21 km

18 5924
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

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