Wednesday, January 29, 2014
BOATS AND STREAMS
IMPORTANT FACTS AND FORMULAE
1.In water ,the direction along
the stream is called downstream and ,the direction against the stream is called
upstream.
2.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.
3.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
SOLVED EXAMPLES
EX.1.A man can row upstream at
7 kmph and downstream at 10kmph.find man’s rate in still water and the rate of
current.
Sol. Rate in still
water=1/2(10+7)km/hr=8.5 km/hr.
Rate of
current=1/2(10-7)km/hr=1.5 km/hr.
EX.2. A man takes 3 hours 45
minutes to row a boat 15 km downstream of a river and 2hours30minutes to cover
a distance of 5km upstream. find the speed of the river current in km/hr.
Sol. rate downstream=(15/3
¾)km/hr=(15*4/15)km/hr=4km/hr.
Rate upstream=(5/2
½)km/hr=(5*2/5)km/hr=2km/hr.
Speed of
current=1/2(4-2)km/hr=1km/hr
EX.3. a man can row 18 kmph in
still water.it takes him thrice as long to row up as to row down the river.find
the rate of stream.
Sol. Let man’s rate
upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=18 or x=9.
Rate upstream=9 km/hr,rate
downstream=27 km/hr.
Hence,rate of
stream=1/2(27-9)km/hr=9 km/hr.
EX.4. there is a road beside a
river.two friends started from a place A,moved to a temple situated at another
place B and then returned to A again.one of them moves on a cycle at a speed of
12 km/hr,while the other sails on a boat at a speed of 10 km/hr.if the river
flows at the speed of 4 km/hr,which of the two friends will return to placeA
first?
Sol. Clearly the cyclist
moves both ways at a speed of 12 km/hr.
The boat sailor moves downstream
@ (10+4)i.e.,14 km/hr and upstream @ (10-4)i.e., 6km/hr.
So,average speed of the boat
sailor=(2*14*6/14+6)km/hr
=42/5 km/hr=8.4 km/hr.
since the average speed of the
cyclist is greater ,he will return ta A first.
EX.5. A man can row 7 ½ kmph in
still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes
to row to a place and back,how far off is the place?
Sol. Speed downstream
=(7.5+1.5)km/hr=9 km/hr;
Speed
upstream=(7.5-1.5)kmph=6kmph.
Let the required distance be x
km.then,
x/9+x/6=50/60.
2x+3x=(5/6*18)
5x=15
x=3.
Hence,the required distance is
3km.
EX.6. In a stream running at
2kmph,a motar boat goes 6km upstream and back again to the starting point in 33
minutes.find the speed of the motarboat in still water.
Sol.let the speed of the
motarboat in still water be x kmph.then,
6/x+2 +6/x-2=33/60
11x2-240x-44=0
11x2-242x+2x-44=0
(x-22)(11x+2)=0
x=22.
EX.7.A man can row 40km
upstream and 55km downstream in 13 hours also, he can row 30km upstream and
44km downstream in 10 hours.find the speed of the man in still water and the
speed of the current.
Sol.let rate upstream=x
km/hr and rate downstream=y km/hr.
Then,40/x +55/y =13…(i) and 30/x
+44/y =10
Multiplying (ii) by 4 and (i) by
3 and subtracting ,we get:11/y=1 or y=11.
Substituting y=11 in (i),we
get:x=5.
Rate in still water
=1/2(11+5)kmph=8kmph.
Rate of
current=1/2(11-5)kmph=3kmph
