Respuesta :
Answer:
Time spent rowing down stream [tex]=100\ seconds[/tex]
Speed of boat in still water [tex]=14\ ms^{-1}[/tex]
Step-by-step explanation:
Let speed of boat in still water be [tex]= x\ ms^{-1}[/tex]
Speed of current [tex]= 10\ ms^{-1}[/tex]
Speed of boat down stream = [tex]\textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}[/tex]
Distance rowed down stream = 2400 m
Time spent rowing down stream = [tex]\frac{Distance}{Speed}=\frac{2400}{x+10}\ s[/tex] = [tex]\frac{Distance}{Speed}=\frac{2400}{x+10}\ s[/tex]
Speed of boat up stream = [tex]\textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}[/tex]
Distance rowed up stream = [tex]\frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m[/tex]
Time spent rowing up stream = [tex]\frac{Distance}{Speed}=\frac{400}{x-10}\ s[/tex]
We know that,
[tex]\textrm{Time spent rowing down stream =Time spent rowing up stream}[/tex]
So,
[tex]\frac{2400}{x+10}=\frac{400}{x-10}[/tex]
Cross multiplying
[tex]2400(x-10)=400(x+10)[/tex]
Dividing both sides by [tex]400[/tex]
[tex]\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}[/tex]
[tex]6(x-10)=x+10[/tex]
[tex]6x-60=x+10[/tex]
Adding 60 to both sides.
[tex]6x-60+60=x+10+60[/tex]
[tex]6x=x+70[/tex]
Subtracting both sides by [tex]x[/tex]
[tex]6x-x=x+70-x[/tex]
[tex]5x=70[/tex]
Dividing both sides by 5.
[tex]\frac{5x}{5}=\frac{70}{5}[/tex]
∴ [tex]x=14[/tex]
Speed of boat in still water [tex]=14\ ms^-1[/tex]
Time spent rowing down stream =[tex]\frac{2400}{14+10}=\frac{2400}{24}=100\ s[/tex]
