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 15 km/h and the rate of current is 13 km/h. Find the distance travelled downstream in 15 min.

Answer:

Explanation:

Distance in downstream = Downstream rate $\times$ time

= $(15+13)\times\frac{15}{60}$ = 7 km/h

The speed of motorboat in still water is 6 km/h. A motor boat goes 7 km upstream and back to the starting point in $2\frac{2}{5}$ hrs. The velocity of the current is 

Answer:

Explanation:

Let velocity of current $=x$ km/h

Upstream speed $=(6–x)$ km\/h

Downstream speed $=(6 + x)$ km/h

$7\times\left(\frac{1}{6-x}+\frac{1}{6 + x}\right)$ $=\frac{12}{5}$

$x$ = 1, -1

$x$ = 1 km/h (negative cannot be speed)

A motor boat goes 15 km against the stream running at 4 km/h and back in 2 hours. The speed in km/h of the motorboat in still  water is 

Answer:

Explanation:

Let speed of motor boat in still water  $=x$ km/h

Downstream speed $=(x+4)$ km/h

Upstream speed  $=(x-4)$ km/h

$\frac{15}{x-4}+\frac{15}{x+4}$ $=2$

$x$ = 16, -1

Speed cannot be negative, so $x$ = 16 km/h

A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Answer:

Explanation:

Downstream speed $=5+1$ $=6$ kmph

Upstream speed $=5-1$ $=4$ kmph

Let the distance be $=x$ km

$\frac{x}{6}+\frac{x}{4}$ $=1$

$x$ $=\frac{12}{5}$ = 2.4 km

A man rows 10 km upstream and back again to the starting point in 55 min. If the speed of stream is 2 km/h, find the speed of rowing in still water.

Answer:

Explanation:

Let speed of rowing in still water $=x$ km/h

Speed of stream = 2 km/h and total time $=\frac{55}{60}$ hrs

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

= Total Distance / ((Upstream rate$\times$ Downstream rate)/ Speed in still water)

$\frac{55} {60}$ = $\frac{x\times 2\times 10} {(x+2)(x- 2)}$

$x$ = 22 (negative value of $x$ is not possible)

Speed of rowing in still water  = 22 km/h

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