Respuesta :
Answer:
The speed on boat in still water is [tex]56 \frac{km}{h}[/tex] and the rate of the current is [tex]10 \frac{km}{h}[/tex]
Explanation:
Since speed , [tex]v= \frac{Distance\, traveled(D)}{Time\, taken(t)}[/tex]
Therefore speed of motor boat while traveling upstream is
[tex]v_{upstream}=\frac{92}{2}\frac{km}{h}=46\frac{km}{h}[/tex]
and speed of motor boat while traveling downstream is
[tex]v_{downstream}=\frac{132}{2}\frac{km}{h}=66\frac{km}{h}[/tex]
Let speed of boat in still water be [tex]v_b[/tex] and rate of current be [tex]v_w[/tex]
Therefore [tex]v_{upstream}=v_b-v_w=46\frac{km}{h}[/tex] ----(A)
and [tex]v_{downstream}=v_b+v_w=66\frac{km}{h}[/tex] ------(B)
Adding equation (A) and (B) we get
[tex]2v_b= (46+66) \frac{km}{h}=112 \frac{km}{h}[/tex]
=>[tex]v_b= 56 \frac{km}{h}[/tex] ------(C)
Substituting the value of [tex]v_b[/tex] in equation (A) we get
[tex]v_w= 10 \frac{km}{h}[/tex]
Thus the speed on boat in still water is [tex]56 \frac{km}{h}[/tex] and the rate of the current is [tex]10 \frac{km}{h}[/tex]
