## Boat and Streams

**Downstream**

In water, the direction along the stream is called downstream.

**Upstream**

In water, the direction against the stream is called upstream.

### Some Basic Formulas:

1. 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

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

Speed in still water=

Rate of stream=

3. A man can row in still water at x km/h. In a stream flowing at y km/h, if he rows the same distance up and down the stream, then his average speed is given by

4. 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

5. 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

6. A man can row certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of stream is y km/h, then the speed of man in still water is given by

7. 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

## Questions Asked from this Chapter:

### Question Type 1: A Boat/Man covers X_{1} Km upstream and Y_{1} Km downstream in H_{1} hours while it covers X_{2} Km upstream and Y_{2} Km downstream in H_{2} hours. Find Speed of Boat & Stream

**Example:**

The speed of a boat in still water is 10 Km/hr. It covers upstream a distance of 45 Km in 6 hours. The speed(in Km/hr) of stream is:

a) 2.5

b) 3

c) 3.5

d) 4

**Solution:**

### Question Type 2: A Boat/Man goes X Km upstream in H1 hours and Y Km downstream in H2 hours. Find Speed of Boat & Stream

**Example:**

A sailer goes 12 Km downstream in 48 minutes and return in 1 hour 20 minutes. The speed of the sailer in still water is:

a) 12 Km/hr

b) 12.5 Km/hr

c) 13 Km/hr

d) 15 Km/hr

**Solution:**

### Question Type 3: A Boat/Man takes 'N' times as much time in going the same distance in opposite direction.

**Example:**

In a fixed time, a boy swims double the distance along the current that he swims against the current. If the speed of the current is 3 km/hr, the speed of the boy in still water is:

a) 6 Km/hr

b) 9 Km/hr

c) 10 km/hr

d) 12 km/hr

**Solution:**