Answer:
- Speed of boat = x = 11miles /hr
- Speed of current = y = 10miles /hr
Step by step explanation:
Here it is given that a boat travelled each way downstream and back . So while going back it would have travelled upstream.
And the time taken to go downstream is 6hrs and that of upstream is 126 hrs . So let us take ,
[tex]\longrightarrow v_{boat}= x \\[/tex]
[tex]\longrightarrow v_{current}= y[/tex]
As we know that ,
While going downstream, the speed will be ,
[tex]\longrightarrow v_d= x + y \dots (i) [/tex]
And while up stream,
[tex]\longrightarrow v_u = x - y\dots (ii)[/tex]
Also , we know that ,
[tex]\longrightarrow v = s\times t , [/tex]
So that, while going downstream,
[tex]\longrightarrow v_d = \dfrac{126}{6}\\ [/tex]
[tex]\longrightarrow v_d = 21 \dots (iii) [/tex]
Again, while going upstream,
[tex]\longrightarrow v_u = \dfrac{126}{126}\\ [/tex]
[tex]\longrightarrow v_u = 1 \dots (iv) [/tex]
From equation (i) and (iii) , we have,
[tex]\longrightarrow x + y = 21 \dots (v)[/tex]
And from (ii) and (iv) , we have,
[tex]\longrightarrow x-y = 1 \dots(vi)[/tex]
On adding equation (v) and (vi) , we have;
[tex]\longrightarrow x+y+x-y = 21 +1 \\[/tex]
[tex]\longrightarrow 2x = 22\\ [/tex]
[tex]\longrightarrow x =\dfrac{22}{2} [/tex]
[tex]\longrightarrow \underline{\underline{x = 11\ miles/hr }} [/tex]
Substitute for x in (vi) ,
[tex]\longrightarrow 11 - y =1\\ [/tex]
[tex]\longrightarrow y = 11-1\\[/tex]
[tex]\longrightarrow \underline{\underline{ y = 10\ miles/hr}}[/tex]
