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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
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 kmphCorrect 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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