## Important Terms for Boats and Streams Formula

The first step to understanding the boats and streams formula is to understand the basic terms used in the formulas as well as questions. Here are the important terms every applicant should know:

- Stream- The water that is moving in the river is called a stream.
- Upstream- When the boat is flowing in the opposite direction of the stream, it is called Upstream.
- Downstream- When the boat is flowing in the same direction as the stream, it is called Downstream
- Still Water- When the water is stationary i.e. not flowing then the speed of water is zero.

## Boats and Streams Formula

Without knowing the accurate boats and streams formula it is impossible for any applicant to solve the question. Every applicant should memorize these and should be on fingertips. Here are some of the important boats and stream formulas:

Upstream | (u−v) km/hr |

Downstream | (u+v)Km/hr |

Speed of Boat in Still Water | ½ (Downstream Speed + Upstream Speed) |

Speed of Stream | ½ (Downstream Speed – Upstream Speed) |

Average Speed of Boat | {(Upstream Speed × Downstream Speed) / Boat’s Speed in Still Water} |

Speed of boat or swimmer in still water | 1/2 (Downstream Speed + Upstream Speed) |

Other Important Boats and stream formulas

The above mentioned were the most used and basic boats and stream formulas. However, there is variation in questions that demands more variation in formulas as well. Here are some other important boats and stream formula:

- Calculating distance between two points, If it takes “t” hours for a boat to reach a point in still water and comes back to the same point
**Distance = {(u2-v2) × t} / 2u** - Calculating the distance between two points, If it takes “t” hours more to go to a point upstream than downstream for the same distance
**Distance = {(u2-v2) × t} / 2v** - Calculate the speed of swimmer or man in still water, If a boat travels a distance downstream in “t1” hours and returns the same distance upstream in “t2” hours
**[v × {(t2+t1) / (t2-t1)}] km/hr**

u= speed of the boat in still water

v= speed of the stream

## Types of Boats and Stream Questions

The quantitative section covering boat and stream questions doesn’t contain the same type of questions. There are 4 types of questions and based on the type, boats and stream formula is applied accordingly:

- Time-based questions
- Speed based questions
- Average speed based questions
- DIstance based questions

**Time-based questions**: As the name suggests, you have to calculate time in this type of question. You will have to calculate the time taken by a boat to travel upstream or downstream.

Example – The speed of a boat is that of the stream as 36:5. The boat goes along with the stream in 5 hours and 10 minutes. How much time will it take to come back?

Solution: 6 5/6

**Speed-based questions**: In this type, you have to calculate the speed of the stream or boat. In this type of question, you might also find variations such as the speed of the boat in still water.

Example – The speed of the boat when traveling downstream is 32 km/hr. whereas when traveling upstream it is 28 km/hr. What are the speed of the boat in still water and the speed of the stream?

Solution : Speed of the boat in still water = 30 km/hr.

Speed of the stream = 2 km/hr.

**Average speed-based questions**: This is the simplest type, the speed of downstream and upstream will be mentioned and you have to find out the average speed. Sometimes, the speed of either one stream is mentioned with the average speed and you will have to calculate the other speed of the other stream.

Example – A boat, while going downstream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. While returning because of water resistance, it took 1 hour 15 minutes to cover the same distance. What was the average speed during the whole journey?

Solution : 48 miles/ hr.

**Distance-based questions**– In this type, you have to calculate the distance traveled by boat upstream or downstream. Usually in this type of question time, speed and stream are mentioned.

Example – A person challenged himself to cross a small river and back. His speed of the boat in still water is 3 km/hr. He calculated the speed of the river that day as 1 km/hr. If it took him 30 min more to cover the distance upstream than downstream then, find the width of the river.

Solution: 2 Km

- 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
^{2}−y^{2}) / 2x km - 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)

**Some Important Shortcuts:**

- Suppose a man can row a boat at a speed of r km/hr in still water and covers the same distance up and down in a stream while a stream flows at a speed of s km/hr. His average speed will be :
- A man rows downstream by covering a certain distance in p1 hours and returns the same distance upstream in p2 hours. If the speed of the stream is s km/hr, then the speed of the man in still water will be :
- A man takes same number of times say m times to row upstream as to row downstream a river. If the speed of the man is r km/hr and the speed of the stream is s km/hr, then

**Type 1: Tips and Tricks for Finding Speed of Boat**

**Boats and Streams Tips and Trick and Shortcuts**

Speed of the boat in still water = 1/2 (Downstream speed + Upstream speed)

Downstream speed = Speed of boat in still water + Speed of stream

Upstream speed = Speed of boat in still water – Speed of stream

**Question 1:A man rows a boat at 12 km/h along the stream and 8 km/h against the stream. Find the speed of the boat in still water.**

**Options:**

**A. 12km/hr**

**B. 10km/hr**

**C. 15km/hr**

**D. 8km/hr**

**Solution: **Downstream speed of the boat = 12 km/h

Upstream speed of the boat = 8 km/h

Speed of the boat in still water = 1/2*(Downstream speed + Upstream speed)

= 1/2 (12 + 8)

= 10 km/h

**Correct option: B**

**Type 2: Tips and Tricks to Find the Speed of Stream**

**Tips and Trick and Shortcuts for Boats and Streams**

Speed of stream = 1/2 *(Downstream speed – upstream speed)

Speed downstream = (u + v ) km/hr.

Speed upstream = (u – v ) km/hr.

**Question 1:A boat whose speed in 15 km/hr in still water goes 30 km downstream and it takes 4 hours 30 minutes to come back. Find the speed of the stream?**

**Options:**

**A . 25km/hr**

**B. 15m/hr**

**C. 20km/hr**

**D. 5km/hr**

**Solution: **Let the speed of the stream = x

Therefore, speed downstream = 15 + x

Speed upstream = 15 – x

30/(15+x) + 30/(15-x) = 4hr 30 min

30/(15+x)+ 30/(15-x) = 9/2

On solving we get

x = 5km/hr

**Correct option: D**

**Type 3: Using Man’s Still Water Speed Calculate Stream’s Speed**

**Question 1:A sailor can row 6 km/h in still water. It takes him twice as long to row up as to row down the river. Find the speed of the stream.**

**Options:**

**A. 6 km/ hr**

**B. 5 km/ hr**

**C. 3 km/ hr**

**D. 2 km/ hr**

**Solution: **Let sailor’s speed in upstream = x

Downstream speed = 2x (As given in the question, his downstream speed is twice of upstream speed)

Man’s speed in still water = 1/2 (Upstream speed + Downstream speed)

= 1/2 (x + 2x) = 3x/2

3x/2 = 6 (sailor can row 6 km/h in still water)

x = 4 km/hr

Therefore, upstream speed = x = 4 km/hr

Downstream speed = 2x = 2 * 4 = 8 km/hr

Speed of stream = 1/2* (Downstream speed – Upstream speed)

= 1/2 (8 – 4)

= 2 km/ hr

**Correct option: D**