Question

The current of a river is 4 miles per hour. A boat travels to a point 16 miles upstream and back in 3 hours. What is the speed of the boat in still water?

Answer 1

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:

`\text{Distance = }(speed)/(time)`

Thus, we have:

`\begin{gathered} Time=(speed)/(dis\tan ce) \\ \\ \\ 3=(16)/((x+4))+(16)/((x-4)) \end{gathered}`

Let's solve for x:

Multiply all terms by (x+4)(x-4)

`\begin{gathered} 3(x+4)(x-4)=(16)/((x+4))\ast(x+4)(x-4)+(16)/((x-4))\ast(x+4)(x-4) \\ \\ 3(x+4)(x-4)=16(x-4)+16(x+4) \end{gathered}`

Solving further:

`\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}`

Equate to zero: