BOAT AND STREAM

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Boat and stream problems is a sub-set of time, speed and distance type questions where in relative speed takes the foremost role. We always find several questions related to the above concept in SSC common graduate level exam as well as in bank PO exam. Upon listing the brief theory of the issue below we move to the various kinds of problems asked in the competitive examination.

Important Formulas – Boats and Streams

• Downstream
  In running/moving water, the direction along the stream is called downstream.
• Upstream
  In running/moving water, the direction against the stream is called upstream.

• Let the speed of a boat in still water be u km/hr and the speed of the stream be v km/hr, then

  Speed downstream = (u+v) km/hr
  Speed upstream = (u – v) km/hr

• Let the speed downstream be a km/hr and the speed upstream be b km/hr, then

  Speed in still water =1/2*(a+b)km/hr
  Rate of stream = 1/2*(a−b) km/hr

Some more short-cut methods

• Assume that a man can row at the speed of x km/hr in still water and he rows the same distance up and down in a stream which flows at a rate of y km/hr. Then his Average speed throughout the journey

  = (Speed downstream × Speed upstream)/Speed in still water=((x+y)(x−y))/xkm/hr

• Let the speed of a man in still water be x km/hr and the speed of a stream be y km/hr. If he takes t hours more in upstream than to go downstream for the same distance, the distance

  =((x* x –y* y)*t)/2ykm

• A man rows a certain distance downstream in t₁ hours and returns the same distance upstream in t₂ If the speed of the stream is y km/hr, then the speed of the man in still water

  =y((t2+t1) / (t2−t1)) km/hr

• A man can row a boat in still water at x km/hr. In a stream flowing at y km/hr, if it takes him t hours to row a place and come back, then the distance between the two places

  =t((x* x –y* y))/2xkm

• A man takes n times as long to row upstream as to row downstream the river. If the speed of the man is x km/hr and the speed of the stream is y km/hr, then

  x=y*((n+1)/(n−1))

Solved Examples

Level 1

Answer : Option B

Explanation :

Man’s speed with the current = 15 km/hr

=>speed of the man + speed of the current = 15 km/hr

speed of the current is 2.5 km/hr

Hence, speed of the man = 15 – 2.5 = 12.5 km/hr

man’s speed against the current = speed of the man – speed of the current

= 12.5 – 2.5 = 10 km/hr

Answer : Option B

Explanation :

Let the speed downstream be a km/hr and the speed upstream be b km/hr, then

Speed in still water =1/2(a+b) km/hr and Rate of stream =1/2(a−b) km/hr
Speed in still water = 1/2(14+8) kmph = 11 kmph.

Answer : Option A

Explanation :

Speed upstream = 2/2=1 km/hr

Speed downstream = 1/(20/60)=3 km/hr

Speed in still water = 1/2(3+1)=2 km/hr

Time taken to travel 5 km in still water = 5/2= 2 hour 30 minutes

Answer : Option C

Explanation :

Speed downstream = (22 + 4) = 26 kmph

Time = 24 minutes = 24/60 hour = 2/5 hour

distance travelled = Time × speed = (2/5)×26 = 10.4 km

Answer : Option B

Explanation :

Let the speed of the boat in still water = x kmph

Given that speed of the stream = 3 kmph

Speed downstream = (x+3) kmph

Speed upstream = (x-3) kmph

He travels a certain distance downstream in 1 hour and come back in 1¹⁄₂ hour.

ie, distance travelled downstream in 1 hour = distance travelled upstream in 1¹⁄₂ hour

since distance = speed × time, we have

(x+3)×1=(x−3)*3/2

=> 2(x + 3) = 3(x-3)

=> 2x + 6 = 3x – 9

=> x = 6+9 = 15 kmph

Answer : Option D

Explanation :

Speed of the boat in still water = 22 km/hr

speed of the stream = 5 km/hr

Speed downstream = (22+5) = 27 km/hr

Distance travelled downstream = 54 km

Time taken = distance/speed=54/27 = 2 hours

Answer : Option B

Explanation :

Speed downstream = 22/4 = 5.5 kmph

Speed upstream = 22/5 = 4.4 kmph

Speed of the boat in still water = (½) x (5.5+4.42) = 4.95 kmph

Answer : Option A

Explanation :

Let speed upstream = x

Then, speed downstream = 2x

Speed in still water = (2x+x)2=3x/2

Speed of the stream = (2x−x)2=x/2

Speed of boat in still water: Speed of the stream = 3x/2:x/2 = 3 : 1

Level  2

Answer : Option C

Explanation :

Speed of the motor boat = 15 km/hr

Let speed of the stream = v

Speed downstream = (15+v) km/hr

Speed upstream = (15-v) km/hr

Time taken downstream = 30/(15+v)

Time taken upstream = 30/(15−v)

total time = 30/(15+v)+30/(15−v)

It is given that total time is 4 hours 30 minutes = 4.5 hour = 9/2 hour

i.e., 30/(15+v)+30/(15−v)=9/2

⇒1(15+v)+1(15−v)=(9/2)×30=3/20

⇒(15−v+15+v)/(15+v)(15−v)=3/20

⇒30/(15*15−v*v)=3/20

⇒30/(225−v*v)=3/20

⇒10/(225−v* v)=1/20

⇒225−v* v =200

⇒v* v =225−200=25

⇒v=5 km/hr

Answer : Option A

Explanation :

Assume that he moves 4 km downstream in x hours

Then, speed downstream = distance/time=4/x km/hr

Given that he can row 4 km with the stream in the same time as 3 km against the stream

i.e., speed upstream = 3/4of speed downstream=> speed upstream = 3/x km/hr

He rows to a place 48 km distant and come back in 14 hours

=>48/(4/x)+48/(3/x)=14

==>12x+16x=14

=>6x+8x=7

=>14x=7

=>x=1/2

Hence, speed downstream = 4/x=4/(1/2) = 8 km/hr

speed upstream = 3/x=3/(1/2) = 6 km/hr

Now we can use the below formula to find the rate of the stream

Let the speed downstream be a km/hr and the speed upstream be b km/hr, then

Speed in still water =1/2*(a+b) km/hr

Rate of stream =12*(a−b) km/hr
Hence, rate of the stream = ½*(8−6)=1 km/hr

Answer : Option C

Explanation :

Let the rate upstream of the boat = x kmph

and the rate downstream of the boat = y kmph

Distance travelled upstream in 8 hrs 48 min = Distance travelled downstream in 4 hrs.

Since distance = speed × time, we have

x×(8*4/5)=y×4

x×(44/5)=y×4

x×(11/5)=y— (equation 1)

Now consider the formula given below

Let the speed downstream be a km/hr and the speed upstream be b km/hr, then

Speed in still water =1/2(a+b) km/hr

Rate of stream =1/2(a−b) km/hr
Hence, speed of the boat = (y+x)/2

speed of the water = (y−x)/2

Required Ratio = (y+x)/2:(y−x)/2=(y+x):(y−x)=(11x/5+x):(11x/5−x)

(Substituted the value of y from equation 1)

=(11x+5x):(11x−5x)=16x:6x=8:3

Answer : Option C

Explanation :

Speed in still water = 5 kmph
Speed of the current = 1 kmph

Speed downstream = (5+1) = 6 kmph
Speed upstream = (5-1) = 4 kmph

Let the requited distance be x km

Total time taken = 1 hour

=>x/6+x/4=1

=> 2x + 3x = 12

=> 5x = 12

=> x = 2.4 km

Answer : Option B

Explanation :

Distance = 3/4 km

Time taken to travel upstream = 11¹⁄₄ minutes

= 45/4 minutes = 45/(4×60) hours = 3/16 hours

Speed upstream = Distance/Time= (3/4)/ (3/16) = 4 km/hr

Time taken to travel downstream = 7¹⁄₂minutes = 15/2 minutes = 15/2×60 hours = 1/8 hours

Speed downstream = Distance/Time= (3/4)/ (1/8) = 6 km/hr

Rate in still water = (6+4)/2=10/2=5 kmph

Answer : Option D

Explanation :

Speed of the boat in still water = 10 mph

Let speed of the stream be x mph

Then, speed downstream = (10+x) mph

speed upstream = (10-x) mph

Time taken to travel 36 miles upstream – Time taken to travel 36 miles downstream= 90/60 hours

=>36/(10−x)−36/(10+x)=3/2=>12/(10−x)−12/(10+x)=1/2=>24(10+x)−24(10−x)=(10+x)(10−x)

=>240+24x−240+24x=(100−x* x)=>48x=100− (x* x)=> x* x +48x−100=0

=>(x+50)(x−2)=0=>x = -50 or 2; Since x cannot be negative, x = 2 mph

Answer : Option D

Explanation :

Let the speed of Rahul in still water be x mph
and the speed of the current be y mph

Then, Speed upstream = (x – y) mph
Speed downstream = (x + y) mph

Distance = 12 miles

Time taken to travel upstream – Time taken to travel downstream = 6 hours

⇒12/(x−y)−12/(x+y)=6

⇒12(x+y)−12(x−y)=6(x*x−y*y)

⇒24y=6(x*x−y*y)

⇒4y= x*x−y*y

⇒x * x =(y* y +4y)⋯(Equation 1)

Now he doubles his speed. i.e., his new speed = 2x

Now, Speed upstream = (2x – y) mph

Speed downstream = (2x + y) mph

In this case, Time taken to travel upstream – Time taken to travel downstream = 1 hour

⇒12/(2x−y)−12/(2x+y)=1

⇒12(2x+y)−12(2x−y)=4*x* x –y* y

⇒24y=4*x* x –y* y

⇒4*x* x = y* y +24y⋯(Equation 2)

(Equation 1 × 4)⇒4x* x =4(y* y +4y)⋯(Equation 3)

(From Equation 2 and 3, we have)

y* y +24y=4(y* y +4y)⇒y* y +24y=4y* y +16y⇒3y* y =8y⇒3y=8

y=8/3 mphi.e., speed of the current = 8/3 mph=2*2/3 mph,

Boating, canoeing, kayaking, rafting, rowing, sailing, stream fishing, and stream swimming are all popular activities that can be enjoyed on a stream. Each activity has its own unique set of challenges and rewards, and the best activity for you will depend on your interests and abilities.

Boating is a general term that refers to any activity that involves using a boat to travel on water. Boats come in a variety of shapes and sizes, and can be powered by paddles, oars, motors, or sails. Boating can be a great way to explore a new area, go fishing, or simply relax on the water.

Canoeing is a type of boating that involves using a canoe, which is a small, lightweight boat that is typically propelled by paddles. Canoes are often used for recreational purposes, such as fishing, camping, and exploring waterways. They can also be used for competitive racing.

Kayaking is a type of boating that involves using a kayak, which is a small, narrow boat that is typically propelled by paddles. Kayaks are often used for recreational purposes, such as fishing, camping, and exploring waterways. They can also be used for competitive racing.

Rafting is a type of boating that involves using a raft, which is a large, inflatable boat that is typically propelled by oars or paddles. Rafts are often used for white-water rafting, which is a thrilling activity that involves navigating rapids and waterfalls.

Rowing is a type of boating that involves using oars to propel a boat through the water. Rowing boats come in a variety of shapes and sizes, and can be used for recreational purposes, such as racing, or for competitive purposes, such as rowing in the Olympics.

Sailing is a type of boating that involves using sails to propel a boat through the wind. Sailboats come in a variety of shapes and sizes, and can be used for recreational purposes, such as cruising, or for competitive purposes, such as racing in the America’s Cup.

Stream fishing is a type of fishing that takes place in a stream. Stream fishing can be a great way to catch a variety of fish, including trout, bass, and panfish. It is important to be aware of the regulations in your area before you go stream fishing, as some streams are closed to fishing or have specific regulations on what type of fish can be caught and how many can be caught.

Stream swimming is a type of swimming that takes place in a stream. Stream swimming can be a great way to cool off on a hot day, but it is important to be aware of the dangers of stream swimming. Streams can be swift and dangerous, and there may be hidden obstacles, such as rocks or logs, that can cause injuries. It is important to swim in a safe area, such as a designated swimming area or a calm section of the stream.

No matter what activity you choose, be sure to take the necessary safety precautions. Always wear a life jacket when boating or swimming, and be aware of the weather conditions. If you are new to an activity, it is a good idea to take a lesson from a qualified instructor. With a little preparation, you can enjoy a safe and enjoyable experience on the water.

What is a river?

A river is a large natural stream of water flowing in a channel to the sea, a lake, or another river.

What are the different types of rivers?

There are many different types of rivers, but some of the most common include:

• Mountain rivers: These rivers are found in mountainous areas and are characterized by their steep slopes and fast-moving water.
• Floodplain rivers: These rivers are found in areas where the land is flat and the water is slow-moving.
• Delta rivers: These rivers are found at the mouth of a river where it meets the ocean.
• Artificial rivers: These rivers are man-made and are often used for Irrigation or transportation.

What are the different parts of a river?

The different parts of a river include:

• Headwaters: The headwaters are the source of the river.
• Watershed: The watershed is the area of land that drains into the river.
• Channel: The channel is the path that the river follows.
• Banks: The banks are the sides of the river.
• Delta: The delta is the area where the river meets the ocean.
• Mouth: The mouth is the point where the river flows into the ocean.

What are the different features of a river?

Some of the different features of a river include:

• Rapids: Rapids are areas of fast-moving water.
• Shoals: Shoals are areas of shallow water.
• Waterfalls: Waterfalls are areas where the river drops over a cliff.
• Islands: Islands are areas of land that are surrounded by water.
• Meanders: Meanders are curves in the river.

What are the different uses of rivers?

Rivers are used for many different purposes, including:

• Transportation: Rivers are often used for transportation, especially in areas where there are no roads.
• Irrigation: Rivers are often used for irrigation, which is the process of watering crops.
• Hydroelectric power: Rivers can be used to generate hydroelectric power, which is a type of RENEWABLE ENERGY.
• Recreation: Rivers are often used for recreation, such as swimming, fishing, and boating.

What are the different threats to rivers?

Some of the different threats to rivers include:

• Pollution: Pollution is a major threat to rivers. It can come from many different sources, such as factories, farms, and cars.
• Deforestation: Deforestation is another major threat to rivers. Trees help to filter water and prevent erosion. When trees are cut down, this can lead to pollution and flooding.
• Dams: Dams are often built on rivers to generate hydroelectric power. However, dams can also have a negative impact on rivers. They can block fish Migration, change the water temperature, and reduce the amount of sediment that is carried downstream.
• Climate change: Climate Change is also a threat to rivers. As the climate changes, the patterns of rainfall and snowfall can change. This can lead to changes in the flow of rivers, which can have a negative impact on the Plants and animals that live in rivers.

What can we do to protect rivers?

There are many things that we can do to protect rivers. Some of the most important things include:

• Reduce pollution: We can reduce pollution by reducing our use of Resources, such as water and energy. We can also recycle and compost to reduce the amount of waste that we produce.
• Plant trees: Trees help to filter water and prevent erosion. We can plant trees in areas that are prone to flooding or erosion.
• Support sustainable agriculture: Sustainable Agriculture is a type of agriculture that does not harm the Environment. We can support sustainable agriculture by buying food from farmers who use sustainable practices.
• Protect wetlands: Wetlands are areas of land that are saturated with water. They help to filter water and prevent flooding. We can protect wetlands by not building on them and by planting native plants in them.
• Educate others: We can educate others about the importance of rivers and how to protect them. We can do this by talking to our friends and family, writing letters to our elected officials, and volunteering with organizations that work to protect rivers.

1. What is the name of the process by which water moves from the Earth’s surface to the Atmosphere?
   (A) Evaporation
   (B) Condensation
   (C) Precipitation
   (D) Runoff

2. What is the name of the force that causes water to move downhill?
   (A) Gravity
   (B) Friction
   (C) Turbulence
   (D) Viscosity

3. What is the name of the process by which water changes from a liquid to a gas?
   (A) Evaporation
   (B) Condensation
   (C) Precipitation
   (D) Runoff

4. What is the name of the process by which water changes from a gas to a liquid?
   (A) Evaporation
   (B) Condensation
   (C) Precipitation
   (D) Runoff

5. What is the name of the process by which water falls from the sky as rain, snow, sleet, or hail?
   (A) Evaporation
   (B) Condensation
   (C) Precipitation
   (D) Runoff

6. What is the name of the process by which water flows over the Earth’s surface?
   (A) Evaporation
   (B) Condensation
   (C) Precipitation
   (D) Runoff

7. What is the name of the process by which water soaks into the ground?
   (A) Infiltration
   (B) Percolation
   (C) Runoff
   (D) Evaporation

8. What is the name of the process by which water moves through the Soil and rocks?
   (A) Infiltration
   (B) Percolation
   (C) Runoff
   (D) Evaporation

9. What is the name of the process by which water moves from the Earth’s surface to the Oceans?
   (A) Evaporation
   (B) Condensation
   (C) Precipitation
   (D) Runoff

10. What is the name of the process by which water moves from the oceans to the Earth’s surface?
    (A) Evaporation
    (B) Condensation
    (C) Precipitation
    (D) Runoff