Answer:
The speed of the boat in still water is 8 miles per hour.
The speed of the current is 4 miles per hour.
Step-by-step explanation:
Let x mph be the speed of the boat in still water and y mph be the speed of the current.
A boat traveled 240 miles downstream, it took him 20 hours. Tavelling downstream, the current "helps" and the speed of the boat is x + y mph. Thus,
[tex]20(x+y)=240[/tex]
A boat traveled 240 miles upstream, it took him 60 hours. Tavelling downstream, the current "interferes" and the speed of the boat is x - y mph. Thus,
[tex]60(x-y)=240[/tex]
Solve the system of two equations:
[tex]\left\{\begin{array}{l}20(x+y)=240\\60(x-y)=240\end{array}\right.\Rightarrow \left\{\begin{array}{l}x+y=12\\x-y=4\end{array}\right.[/tex]
Add these two equations:
[tex]x+y+x-y=12+4\\ \\2x=16\\ \\x=8\ mph[/tex]
Subtract these two equations:
[tex]x+y-(x-y)=12-4\\ \\x+y-x+y=8\\ \\2y=8\\ \\y=4\ mph[/tex]
The speed of the boat in still water is 2 miles per hour
The speed of the current is 4 miles per hour
The calculation can be one as follows
let a represent the speed of the boat
let b represent the speed of the current
20(a+b)= 240...........equation 1
60(a+b)..........equation 2
a + b= 12..........equation 3
a - b= 4.............equation 4
Add both equation 3 and 4 together
(a + b) + (a - b)= 12+4
2x = 16
a= 16/2
a= 8
Subtract equation 4 from equation 3
(a + b) - (a-b)= 12-4
2b= 8
b= 8/2
b= 4
Hence the speed of the boat is 2 miles per hour and the speed of the current is 4 miles per hour.
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