19.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
