In this section, the following topics are discussed with examples

**Downstream****Upstream****Basic Formulae****Examples**

In streams there are two types of concepts,

**DOWNSTREAM**

One moving in the direction of water (i.e) the water will always flow down from a hill right ! So downstream is calculated when the boat is coming down from the hill.

**UPSTREAM**

The other is moving in the direction against the water. As I said the water will always flow down from the hill top so to reach a hill top through a stream we want to always go against the motion of water that is called as UPSTREAM.

#### Basic Concept

Let us consider

S_{B}= Speed of the boat in still water

S_{S }= Speed of water/stream/current

Speed of water downstream **S**_{D}= S_{B }+ S_{S}

Speed of water upstream **S**_{U}=S_{B }– S_{S}

The speed of the boat in still water **S**_{B}= (S_{d} + S_{u}) / 2

The speed of the boat in stream **S**_{S} =(S_{d} – S_{u}) / 2

## The ability to simplify seems to eliminate the unnecessary so that the necessary may speak.

Hans Hoffman

#### Example 1:

The speed of the boat with the current is found to be 15km/hr and the speed of the current is 5 km/hr.Find the speed of the boat moving against the current.

**Sol:**

Speed = 15 km/hr

Speed = 5km/hr

Speed of the boat in the current=speed of the boat+Speed of the current

15 = Speed of the boat + 5

Speed of the boat = 10 km/hr

Boat’s speed against the current=Speed of the boat-Speed of the current

=10-5

= 5 km/hr

#### Example 2:

A boatman goes 4km against the current of the stream in 4 hour and goes 1 km along the current in 20 minutes. How long it will take to go for 7 km in still water?

**Given**

Distance in upstream=4 km

Time taken in upstream=4 hr

Distance in downstream=1 km

Time taken in downstream=20 min

=20/60 hr

=1/3 hr

To find

Time taken for 7 km in still water=?

**Sol**

Speed in upstream =Distance/Time

=4/4

=1 km/hr

Speed in downstream=1/1/3

=3 km/hr

speed in still water=

=2 km/hr

The boat can travel 2km in 1 hr

i.e.,2 km= 1 hr

1 km=30 min

Therefore,7 km=3 hr 30 min

#### Example 3:

A man can go 24 km upstream and 36 km downstream in 6 hrs and also he can row 36 km upstream 24 km downstream in 61/2 hours. Find the rate of current.

**Given**

D_{U1 }=24 km

D_{D1}=36 km

T_{1}=6 hrs

D_{U2}=36 km

D_{D2}= 24 km

T_{2}=6.5 hrs

To find

Rate of current=?

Sol

W.K.T.

T=D/S

Let us consider SU and SD as x and y

24/x+36/y=6

36/x+24/y=6.5

Take 1/x= a and 1/y=b

24a +36b=6

4a+6b=1 ——-(1)

36a+24b=6.5 —–(2)

Solve (1) and (2)

(1) * 9 36a+54b=9

(2) 36a+24b=6.5

30b=2.5

b=2.5/30

b=1/12

Sub b in (1)

4a+6(1/12)=1

8a+1=2

8a=1

a=1/8

Therefore, x=8 and y=12

Rate of current=(12-8)/2

=2km/hr.