Respuesta :
Answer:
The speed of the current is [tex]\frac{1}{30}[/tex] miles/min
The speed of the swimmer is [tex]\frac{1}{60}[/tex] miles/min
Step-by-step explanation:
Let's assume
speed of the current is x miles /min
speed of the swimmer is y miles/min
Swimming downstream a swimmer can cover o.5 mile in 10 minutes
so, we get equation as
[tex]x+y=\frac{0.5}{10}[/tex]
[tex]x+y=0.05[/tex]
it takes the swimmer 30 minutes to swim back up
so, we get equation as
[tex]x-y=\frac{0.5}{30}[/tex]
[tex]x-y=\frac{5}{300}[/tex]
[tex]x-y=\frac{1}{60}[/tex]
So, we get system of equations as
[tex]x+y=0.05[/tex]
[tex]x-y=\frac{1}{60}[/tex]
we can add both equations
and we get
[tex]y=\frac{1}{60},\:x=\frac{1}{30}[/tex]
So,
The speed of the current is [tex]\frac{1}{30}[/tex] miles/min
The speed of the swimmer is [tex]\frac{1}{60}[/tex] miles/min
