## Saturday, July 18, 2015

### Boats and Streams: 8 Important Shortcuts & Tricks Explained with Examples

Stream: Moving water of the river is called stream.
Still Water: If the water is not moving then it is called still water.
Upstream: If a boat or a swimmer moves in the opposite direction of the stream then it is called upstream.
Downstream: If a boat or a swimmer moves in the same direction of the stream then it is called downstream.

Points to remember
i. When speed of boat or a swimmer is given then it normally means speed in still water.
ii. If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,
Speed of boat or swimmer upstream = (x − y) km/h
Speed of boat or swimmer downstream = (x + y) km/h
iii. Speed of boat or swimmer in still water is given by
= 1/2(Downstream + Upstream)
Speed of stream is given by
= 1/2(Downstream - Upstream)

Some Shortcut Methods

Trick-1:
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
= y*(t2 + t1) / (t2 - t1)
Ex: A man can row certain distance downstream in 2 hours and returns the same distance upstream in 4 hours. If the speed of stream is 5 km/h, then the speed of man in still water ?
a. 15     b. 10      c. 12      d. 20
Sol: = 5*(4+2)/(4-2) = 15 km/hr

Trick-2:
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
= y*(t2 - t1) / (t2 + t1)
Ex : Ramesh can row a certain distance downstream in 6 hours and returns the same distance in 9 hours. If the speed of Ramesh in still water is 12 kmph. Find the speed of the stream?
a. 2.4     b. 10      c. 1.2      d. 20

Sol : Speed of the stream =
12 ( 9-6) /(9+6)
= 2.4 kmph

Trick-3:
A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes him 't' hours to row to a place and come back, then the distance between two places is given by
= [ t*(x^2 - y^2)]/(2 * x)
Ex: A man can row in still water at 4 km/h. In a stream flowing at 2 km/h, if it takes him '5' hours to row to a place and come back, then the distance between two places ?
a. 15     b. 10      c. 12      d. 7.5
Sol : [5*(16-4)]/(2*4)=7.5 km

Trick-4:
A man can row in still water at x km/h. In a stream flowing at y km/h, if it takes t hours more in upstream than to go downstream for the same distance, then the distance is given by
= [ t*(x^2 - y^2)]/(2 * y)
Ex: A man can row in still water at 4 km/h. In a stream flowing at 2 km/h, if it takes 3 hours more in upstream than to go downstream for the same distance, then the distance swims by person ?
a. 15     b. 9      c. 12      d. 7.5
Sol : [3*(16-4)]/(2*2)=9 km

Trick-5:
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
= (x^2 - y^2)/x
= (Downstream * Upstream)/man speed in still water.
Ex: A man can row in still water at 4 km/h. In a stream flowing at 2 km/h, if he rows the same distance up and down the stream, then his average speed ?
a. 6     b. 9      c. 3     d. 7.5
Sol : (16-4)]/4 = 3 km/hr

Trick-6:
A man can row a distance 'D' upstream in t1 hrs. If he rows the same distance  down the stream in t2 hrs. then speed is given by
Stream speed = [D*(t1-t2)]/(2*t1*t2)
Ex: A man can row a distance 30 km upstream in 5 hrs. If he rows the same distance  down the stream in 3 hrs. then speed of stream ?
a..8     b. 4      c. 2     d. 6
Sol : [30*(5-3)]/(2*5*3)= 2 km/hr

Trick-7:
A man can row a distance 'D' upstream in t1 hrs. If he rows the same distance  down the stream in t2 hrs. then speed is given by
Man speed = [D*(t1+t2)]/(2*t1*t2)
Ex: A man can row a distance 30 km upstream in 5 hrs. If he rows the same distance  down the stream in 3 hrs. then speed
of man  ?
a. 8     b. 4      c. 2     d. 6
Sol : [30*(5+3)]/(2*5*3)= 8 km/hr