Question

10.
werdges years hence.
(TS - March 2019)
A boat goes 30km upstream and 44km downstream in 10 hours. in 13 hours it can go 40km upstream
and 55 km downstream. Determine the speed of the stream and that of the boat in still water. (Conn)
10.​

Answer 1

Answer:

I don't know but please follow me....

Answer 2

Answer:

SPEED OF BOAT IN STILL WATER = 8 KM/HR

SPEED OF THE STREAMER             = 3 KM/HR

Step-by-step explanation:

LET THE SPEED OF THE BOAT IN STILL WATER BE  X KM/HR

LET THE SPEED OF THE STREAMER BE                      Y KM/HR

SO, SPEED IN DOWN STREAM = X+Y

      SPEED IN UP STREAM        = X-Y

GIVEN,

50 KM UPSTREAM AND 44 KM DOWNSTREAM IN 10 HR

SO,

TIME TO GO 30 KM UPSTREAM + TIME TO GO 44 KM DOWNSTREAM = 10 HR

WE KNOW THAT,

s = d/t

t = d/s

DISTANCE OF 30 KM/SPEED UPSTREAM + DISTANCE OF 44 KM/SPEED DOWN STREAM =10

SO,

30/X-Y + 44/X+Y = 10  ------------ EQUATION 1

SIMILARLY GIVEN,

A BOAT TRAVELS 40 KM UPSTREAM AND 55 KM DOWNSTREAM IN 13 HR

SO,

40 KM UPSTREAM TIME + 55 KM DOWNSTREAM = 13 HR

WE KNOW THAT,

s = d/t

t = d/s

DISTANCE OF 40 KM/SPEED UPSTREAM + DISTANCE OF 55 KM/SPEED DOWN STREAM =13

SO,

40/X-Y+55/X+Y=13-------------EQUATION 2

SO,

EQUATION 1=> 30(1/X-Y) + 44(1/X+Y) = 10

EQUATION 2=>40(1/X-Y) + 55(1/X+Y) = 13

LET,

(1/X-Y) = U

(1/X+Y) = V

SO OUR EQUATION BECOMES,

EQUATION 1=> 30U + 44V = 10

EQUATION 2=> 40U + 55V = 13

SOLVING EQUATION 1 AND 2

FROM 1] 30U + 44V = 10

              30U = 10 - 44V

                 U  =  10 - 44V/30

PUTTING THE VALUES IN EQUATION 2

40U + 55V = 13

40(10 - 44V/30) + 55V = 13

4(10 - 44V/3) + 55V = 13

MULTIPLY IT BY 3 FOR BOTH THE SIDES

3*4(10 - 44V/3) + 3*55V = 13*3 (SOLVE)

4(10 - 44V) + 165V = 39

40 - 176V+165V = 39

-176V+165V =39-40

-11V = -1

V = 1/11

PUT V = 1/11 IN EQUATION 1

30U + 44V = 10

30U + 44*1/11 = 10

30U + 4 + 10

30U = 10 - 4

30U = 6

 U   = 6/30

  U   = 1/5

SO,

U = 1/5 AND V = 1/11

WE NEED TO FIND X AND Y

U   = 1/X-Y

1/5 = 1/X-Y

X-Y = 5 ----------EQUATION 3

V  = 1/X+Y

1/11= 1/X+Y

X+Y = 11 ---------EQUATION 4

ADD EQUATION 3 WITH EQUATION 4

X-Y = 5

X+Y = 11

=> (X+Y) + (X-Y) = 5 + 4

=>  2X                = 16

=>  X                   = 16/2

=>  X                   = 8

SUBSTITUTE EQUATION 4 WITH X = 8 TO GET Y

X+Y = 11

8+Y = 11

Y     =  11 - 89 = 3

SO,

SPEED OF BOAT IN STILL WATER = 8 KM/HR

SPEED OF THE STREAMER             = 3 KM/HR

HOPE IT HELPS YOU

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