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

The speed of boat in still water is 20 km/h, if it can travel 16 km upstream in 1 h. What time it would take to travel the same distance downstream?

Answer:

Explanation:

Speed = $\frac{Distance}{Time}$

Speed of current is $x$ km/h

Upstream speed $= 20–x$

$\therefore x$ = 4 km/h

Let it takes  $y$ hrs to travel downstream

Downstream speed $=20+x$ $=\frac{16}{y}$

$24=\frac{16}{y}$

$y=\frac{2}{3}$ hrs = 40 min.

A boat takes 19 h for travelling downstream from point A to point B and coming back to point C, midway between A and B. If velocity of the stream is 4 km/h and the speed of the boat in still water is 14 km/h. What is the distance between A and B ?

Answer:

Explanation:

Speed downstream $=14+4$ = 18 km/h

Speed upstream $=14-4$ = 10 km/h

Let the distance travelled between $A$ and $B$ be $x$ km

Then $\frac{x}{18}+\frac{x/2}{10}$ = 19

$x$ = 180 km/h

Speed of boat in standing water is 9 km/h and the speed of the stream is 1.5 km/h. A man rows to place at distance of 105 km and comes back to the starting point. The total time taken by him is :

Answer:

Explanation:

Speed upstream = 7.5 km/h

Speed downstream = 10.5 km/h

Total time taken = $\frac{105}{7.5}+\frac{105}{10.5}$ = 24 hrs.

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is 

Answer:

Explanation:

Let  man’s rate upstream $=x$ km/h

Doenstream rate $=2x$ km/h

Speed in still water : Speed of stream

$\frac{2x + x}{2}:\frac{2x - x}{2}$ = 3:1

A motor boat can travel at 10 km/h in still water .If travelled 91 km downstream in a river and then returned ,taking altogether 20 hrs .Find the rate of flow of river 

Answer:

Explanation:

Speed of boat in still water = 10 km /h

Let rate of flow of river $=y$ km/h

Total time = $\frac{Total\quad Distance} {Average\quad Speed}$

= $\frac{Total\quad Distance\times Speed\quad in\quad still\quad water} {Upstream\quad Downstream}$

$20=$ $\left(\frac{2\times 91\times 10} {(10+y)(10-y)}\right)$

 $y$ = 3 km/h

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