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
SB= Speed of the boat in still water
SS = Speed of water/stream/current
Speed of water downstream SD= SB + SS
Speed of water upstream SU=SB – SS
The speed of the boat in still water SB= (Sd + Su) / 2
The speed of the boat in stream SS =(Sd – Su) / 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
DU1 =24 km
DD1=36 km
T1=6 hrs
DU2=36 km
DD2= 24 km
T2=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.