Question

a boat can go 12km upstream and 40km downstream in 8hours.Also it covers 16km upstream and 32km downstream in 8hours.Find the speed of the boat in still water and the speed of the stream


plzzz it is urgent
and ans according to the ncert maths text book for class 10​

Answer 1

Answer:

Let the speed of boat in still water =x

km/h

Let the speed of stream be t km/g

Let upstream be (x-y)km/h

Let downstream be (x+y)km/h

Condition 1

Speed =distance /time

Time=distance /speed

T1=d1/speed upstream

=12/x-ykm/h

T2=d2/speed downstream

=40/x+ykm/h

T1+T2=8h

12/x-ykm/h+40/x+y km/h=8h_ 1equation

Condition 2

Time=Distance /speed

T1=d1/speed upstream

=16/x-ykm/h

T2=d2/speed downstream

=32/x+ykm/h

T1+T2=8h

16/x-ykm/h+32/x+ykm/h=8h_equation 2

By Elimination Method

12/x-y+40/x+y=8

16/x-y+32/x+y=8

let A=1/x-y, B=1/x+y

12A+40B=8

16 A+32B=8

Multiply by 4in 1eq and 3 in 2equation

48A+160B=32

48A+96B =24 subtracting

- - -

0 64B= 8

B=1/8

put B in 1eq

12A+40×1/8=8

12A=8-5

A=1/6

As we know that

A=1x-y , B=1x+y

1/6=1x-y ,1/8=1x+y

x-y=6 , x+y=8

x-y=6

x+y=8dad

+ + +

2x=14

x=7

put yin eq 3

x-y=6

7-y=6

y=1

x=7

y=1