Arithmetic aptitude :: Boats and Streams :: General Questions

• Boats and Streams - General Questions
• Boats and Streams - Data Sufficiency 1
• Boats and Streams - Data Sufficiency 2
• Boats and Streams - Important Formulas and Facts

Still water : The speed of water in the river is zero.

Stream water : The water in the river is flowing or moving.

Speed of Boat and Stream :

Assume the man's rate of rowing in still water $=x$ km/hr Speed of stream $= y$ km/hr

(a) Down stream rate $=(x+y)$ km/hr

(i.e.) direction of rowing and direction of flow is same.

(b) Up stream rate $=(x-y)$ km/hr

(i.e.) direction of rowing and direction of stream are opposite. Speed of still water and stream : Assume, speed downstream $=a$ km/hr

Speed upstream $=b$ km/hr

Then, speed in still water $=\frac{1}{2}(a + b)$ km/hr

Rate of stream $=\frac{1}{2}(a - b)$ km/hr

A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is :

Answer:

Explanation:

Suppose he moves 4 km downstream in $x$ hours. Then,

Speed downstream $=\frac{4}{x}$ km/hr, Speed upstream $=\frac{3}{x}$ km/hr

$\left(\frac{48}{\frac{4}{x}}\right)+\left(\frac{48}{\frac{3}{x}}\right)$ $=14$ or $x=\frac{1}{2}$

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

Rate of the stream $=\frac{1}{2}(8-6)$ km/hr = 1 km/hr.

A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is :

Answer:

Explanation:

Let the speed of the stream be $x$ mph. Then,

Speed downstream $=(10+x)$ mph, Speed upstream $=(10-x)$ mph.

$\frac{36}{( 10 - x )}-\frac{36}{( 10 + x )}$ $=\frac{90}{60}$

$\Leftrightarrow$ $72x\times 60$ $=90(100-x^{2})$

$\Leftrightarrow$ $x^{2}+48x+100$ $=0$

$(x+50)(x-2)=0$ $\Leftrightarrow x$ = 2 mph.

The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is :

Answer:

Explanation:

Let the speed of the stream be $x$ km/hr. Then,

Speed downstream $=(10+x)$ km/hr, Speed upstream $=(10-x)$ km/hr.

$\frac{26}{(10 + x)}$ $=\frac{14}{( 10 - x )}$

$\Leftrightarrow 260 - 26x$ $=140 + 14x$  

$\Leftrightarrow 40x=120$ $\Leftrightarrow x$ = 3 km/hr.

A motorboat, whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is :

Answer:

Explanation:

Let the speed of the stream be $x$ km/hr.Then,

Speed downstream $=(15+x)$ km/hr, Speed upstream $=(15-x)$ km/hr

$\frac{30}{(15+x)}+\frac{30}{(15-x )}$ $=4\frac{1}{2}$  

$\Leftrightarrow \frac{900}{(225-x^{2})}$ $=\frac{9}{2}$

$\Leftrightarrow 9x^{2}$ $=225$

$x^{2}$ $=25$ $\Leftrightarrow x$ = 5 km/hr.

A man swims downstream 40 km in 4 hours and upstream 24 km in 3 hours. Find his speed in still water.

Answer:

Explanation:

Downstream speed $=\frac{40}{4}$ $=10$ km/hr

Upstream speed $=\frac{24}{3}$ $=8$ km/hr

Speed in still water $=\frac{1}{2}(10 + 8)$ = 9 km/hr.

• Boats and Streams - General Questions
• Boats and Streams - Data Sufficiency 1
• Boats and Streams - Data Sufficiency 2