Calculation of Boat speed in Upstream and Down stream water using simple formulas

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Definitions:

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

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

Speed downstream = (a + b) km/hr.
Speed upstream = (a- b) km/hr.

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

Speed in still water = 1/2(a + b) km/hr.
 Rate of stream = 1/2(a - b) km/hr.

Examples 1: If a boat travels 8 km upstream in 24 minutes and speed of stream in 4 kmph. Then what is the speed of boat in still water?

 A. 26kmph  

 B.22 kmph

 C.24 kmph

 D.29 kmph

Solution: As you know of boat  travles 8 km in 24 minutes, you can find the upstream speed 

8 km - 24 min

? km - 60 min 

= (60/24)X8=20 km=20km/hr=20kmph

Still water speed=upstream speed+speed of the stream(by modifying above forumula Speed upstream = (a- b) km/hr.)

=20+4

=24 kmph

Correct answer is C

Example 2: A boat can travel with speed of 24 km/hr ins still water. Speed of the stream is 4 km/hr. Find the time taken by boat to travel 68 km upstream

 A) 4.3 hrs B) 3.4 hrs C) 3.8 hrs D) 4.4 hrs 

Solution:  We have to first find out upstream speed in order to calculate time. 

             upstream speed=still water speed-stream speed

= 24-4=20.

So boat travels with 20 kmph upstream. which means 20 km in 1  hour

20 km  - 60 min

68 km -  ?

=(68/20)X60=204 min

=204/60=3.4 hrs

So the correct answer is B

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