Question

The speed of a stream is 2 mph. A boat travels 6 miles upstream in the same time it takes to travel 10 miles downstream. What is the speed of the boat in still water?

Answer 1

The speed of the boat in still water is 8 mph

Here, we want to get the speed of the boat in still water

Here, we are going to bs using two speeds

The speed in moving water and the speed in still water

Let the speed of the boat in still water be x mph

The speed of the boat downstream is (x + 2) mph

The speed of the boat upstream is (x-2) mph

Mathematically,

`\text{time = }\frac{dis\tan ce}{\text{speed}}`

From the question, we are told that the time taken to travel both upstream and downstream is the same

The time downstream is;

`\text{time = }\frac{10}{x\text{ + 2}}`

The time upstream is;

`\text{time = }(6)/(x-2)`

Since the times are equal, we equate the two as follows;

`\begin{gathered} (10)/(x+2)\text{ = }(6)/(x-2) \\ 10(x-2)\text{ = 6(x+2)} \\ 10x-20\text{ = 6x+12} \\ 10x-6x\text{ = 12 + 20} \\ 4x\text{ = 32x } \\ x\text{ = }(32)/(4) \\ x\text{ = 8 mph} \end{gathered}`