Question

explain please
ans: 6(2/3) km

Answer 1

a 6 (2/3) km because he go fast

Answer 2

Let the speed of the boat be 'x'
and let speed of the river be 'y'.
speed of boat in upstream=x-y
speed of boat in downstream=x+y
We know that,
Time taken=Distance covered/speed

Therefore,
time taken to cover 18km upstream=
18/(x-y)
time taken to cover 18km downstream=
18/(x+y)
As per given condition we have,
18/(x+y)+9=18/(x-y)
18/(x-y)-18/(x+y)=9.................................1

Now rishu doubles his speed,
therefore,speed of boat=2x
Now,
speed of the boat in upstream=2x-y
speed of the boat in downstream=2x+y
time taken to cover 18km upstream=
18/(2x-y)
time taken to cover 18km downstream=
18/(2x+y)
As per given condition we have,
18/(2x+y)+1=18/(2x-y)

18/(2x-y)-18/(2x+y)=1..............................2
solving eq1 we have,
18/(x-y)-18/(x+y)=9

18(x+y)-18(x-y)=9x^2-9y^2

4y=x^2-y^2................................................3

Now , solving eq2 we have,
18/(2x-y)-18/(2x+y)=1

18(2x+y)-18(2x-y)=4x^2-y^2

36y=4x^2-y^2.............................................4

By eq3-eq4 we have,
x^2-y^2-4x^2+y^2=4y-36y

3x^2=32y

x^2=32y/3....................................................5
Putting eq5 in eq3 we get,
32y/3-y^2=4y

32/3-y=4

32/3-4=y

y=20/3...........................................................6
putting eq6 in eq5 we get,
x^2={32(20/3)}/3

x^2=640/9

x=±8√10/3
Here x>0,
therefore x=8√10/3

Hence speed of water = 20/3
=6(2/3) km/hr
and speed of boat at first instance=8√10/3 km/hr
and at second instance=2x=16√10/3 km/hr.