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solve this maths QUEStion ....
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Answers
Answer:
Speed of boat = 8km/hr
speed of stream = 3km/hr
Step-by-step explanation:
Let the speed of boat in still water=x km\hr
Let speed of stream=y km\hr
Speed of boat in downstream=(x+y)km/hr
Speed of boat in upstream=(x−y)km/hr
(time=speed×distance)
Time taken to cover 30 km upstream => 30/x−y
Time taken to cover 44 km downstream=>44/x+y
According to the 1st condition,
⇒30/x−y=44/x+y=10
Time taken to cover 40 km upstream =>40/x−y
Time taken to cover 55 km downstream =>55/x+y
According to the 2nd condition,
⇒40/x−y=55/x+y=13
Let,
1/x−y=v
and
1/x+y=u
=>30u+44v=10..................eq(1)
=>40u+55v=13..................eq(2)
Multiplying eq(1) by 5 and eq(2) by 4 and subtract both
=>150u + 220v = 50
−160u - 220v = -52
=>−10u=−2
=>u=1/5
put u=1/5 in eq(1)
=>30×1/5+44v=10
=>44v=10-6
=>44v=4
=>v=1/11
=>u= 1/x−y = 1/5
=>x−y=5.................eq(3)
=>v = 1/x+y=1/11
=>x+y=11..................eq(4)
adding eq(3) and eq(4)
we get,
=>(x+y)+(x-y)=11+5
=>2x=16
=>x=8
Put x=8 in eq(3)
=>8-y=5
=> y=3
hence speed of boat in still water is 8km/hr
and speed of stream is 3km/hr
Step-by-step explanation:
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