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PREPINSTA PRIME

# Formulas for Boats And Streams

## Boats and Streams Formulas

Boats and streams is one of the most common topics in quantitative section of all the job entrance exams.It is also included in Aptitude section of many job test in companies like TCS, Infosys etc.

**Formulas for Boats and Streams Questions with Basic Concepts **

**1.What is Downstream : **It is related to the direction of water flow in respect with the object, when the object or body is flowing in direction of stream it is called as Downstream

**2. What is Upstream : **It is also related to the direction of water flow in respect with the object, when the object or body is flowing in opposite direction then the stream is called upstream.The boats and streams problems are based on the concepts of time, speed, and distance. However, a few adjustments need to be made in case of such problems. There are two variations of these problems.

Below are the best formulas of boats and Streams problems in seconds.

## Basic Formulas for Upstream and Downstream

If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then

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

If the speed downstream is a km/hr and the speed upstream is b km/hr, then

**Speed in still water **

| 1 | (a + b) km/hr | ||

2 |

**Rate of stream**

| 1 | (a – b) km/hr | ||

2 |

Lets 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** is :

= | | (Speed Downstream)*(Speed Upstream) | |||

Speed in Still Water |

= | | (x + y)*(x – y) | |||

x |

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 travelled is

= | | (x^{2} – y^{2})*t | |||

2y |

A man rows a certain distance downstream in t_{1} hours and returns the same distance upstream in t_{2} hours. If the speed of the stream is y km/hr, then **the speed of the man in still water**

= | | y(t_{2} + t_{1}) | |||

(t_{2} – t_{1}) |

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 is**

= | | t(x^{2} – y^{2}) | |||

2x |

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