Answer:
The rate of the boat in still water is 40 miles per hour
The rate of the current is 10 miles per hour
Step-by-step explanation:
we know that
The speed or rate is equal to divide the distance by the time
Let
x ----> the rate of the current (miles per hour)
y ----> the rate of the boat in still water (miles per hour)
we have that
going upstream
[tex]y-x=\frac{150}{5}[/tex]
[tex]y-x=30[/tex] ----> equation A
going downstream
[tex]y+x=\frac{150}{3}[/tex]
[tex]y+x=50[/tex] ----> equation B
Solve the system of equations by elimination
Adds equation A and equation B
[tex]y-x=30\\y+x=50\\------\\y+y=30+50\\2y=80\\y=40[/tex]
Find the value of x
[tex]y+x=50[/tex]
[tex]40+x=50[/tex]
[tex]x=10[/tex]
therefore
The rate of the boat in still water is 40 miles per hour
The rate of the current is 10 miles per hour
