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Boats and Streams
The water of a stream, usually, keeps flowing at a certain speed, in a particular direction. This speed is called the current of the stream. A boat develops speed because of its engine power. The speed with which it travels when there is no current is called speed of boat in still water. When the boat moves in the direction of the current is said to be with the stream/ current or downstream. When the boat moves in the direction opposite to that of the current, it is said to be against the stream is called upstream.
Eg:-If the speed of a boat in still water is ‘u’km/hr and the speed of the stream is ‘v’km/hr then:
* Speed downstream=(u+v)km/hr
* Speed upstream = (u-v)km/hr
If the speed downstream is u km/hr and the speed upstream is v km/hr, then:
* Speed of boat in still water = ½(u+v)km/hr
* Speed (Rate) of stream = ½ (u-v)km/hr
a) A man can row a boat 12 km/h with the stream and 8km/h against the stream.
Find his speed in still water.
Solution: Speed of boat in still water = ½(u+v) km/hr = ½ (12+8)=10km/hr
b) A man can row a boat 27km/h with the stream and 11km/h against the stream.
Find speed of stream
Solution: Speed (Rate) of stream = ½ (u-v) km/hr = ½ (27-11)=8km/hr
c) A boat running downstream covers a distance of 16km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
d) None of these
Rate of downstream=(16/2 ) kmph=8kmph
Rate of upstream =(16/4) kmph=4kmph
Therefore Speed in still water=1/2(8+4) kmph=6kmph
Note: If ratio of downstream and upstream speeds of a boat is ‘a:b.’
Then ratio of time taken= b:a
Speed of stream=a-b/a+b *Speed in still water
Speed in still water =a+b/a-b *Speed of stream
1. A man rows downstream 32 km and 14km upstream. If he takes 6 hours to cover each distance, then the velocity (in kmph) of the current is:
Solution: Rate downstream=(32/6)kmph; Rate upstream=(14/6)kmph
Velocity of current=1/2(32/6-14/6)kmph=3/2kmph=1.5kmph
2. In one hour, a boat goes 11km along the stream and 5km against the stream.
The speed of the boat in still water (in km/hr)is:
Solution: Speed in still water=1/2(11+5)kmph=8kmph
3. Speed of a boat in still water is 16km/h. If it can travel 20km downstream in the same time as it can travel 12 km upstream, the rate of stream is.
Solution: Speed downstream: Speed upstream=20:12=5:3
Speed of current=5-3/5+3*16=4km/h