Given:
Current of the river = 4 miles per hour
Distance the boat travelled = 16 miles
Time = 3 hours
Let's find the speed of the boat.
Let x represent the speed of the boat.
Thus, we have:
Speed of boat upstream = x - 4
Speed of boat downstream = x + 4
Apply the distance formula:
[tex]\text{Distance = }\frac{speed}{time}[/tex]Thus, we have:
[tex]\begin{gathered} Time=\frac{speed}{dis\tan ce} \\ \\ \\ 3=\frac{16}{(x+4)}+\frac{16}{(x-4)} \end{gathered}[/tex]Let's solve for x:
Multiply all terms by (x+4)(x-4)
[tex]\begin{gathered} 3(x+4)(x-4)=\frac{16}{(x+4)}\ast(x+4)(x-4)+\frac{16}{(x-4)}\ast(x+4)(x-4) \\ \\ 3(x+4)(x-4)=16(x-4)+16(x+4) \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} 3(x(x-4)+4(x-4))=16(x)+16(-4)+16(x)+16(4) \\ \\ 3(x^2-4x+4x-16)=16x-64+16x+64 \\ \\ 3(x^2-16)=16x+16x-64+64 \\ \\ 3x^2-16=32x \end{gathered}[/tex]Equate to zero:
