Question

What is the speed of the boat in still water ?

Answer 1

Step 1

Let a = speed of the boat in still water

Let c = Speed of current

Upstream;

`\begin{gathered} speed\text{ = }a-c \\ d_u=(a-c)t_u \end{gathered}`

Downstream;

`\begin{gathered} \text{Speed}=\text{ a+c } \\ d_d=(a+c)t_d \end{gathered}`

Step 2

Given that

`\begin{gathered} d_d=24\text{ miles} \\ d_u=\text{ 16 miles} \\ t_u=4\text{ hours} \\ t_d=\text{ 2 hours} \end{gathered}`

Hence;

`\begin{gathered} 24=(a+c)2----(1) \\ 16=(a-c)4---(2) \\ 24\text{ = 2a+2c} \\ 16=4a-4c \end{gathered}`

Step 3

Multiply equation 1 by 4 and equation 2 by 2, then add equations 1 to 2 to get the value of a

Hence,

`\begin{gathered} (16a)/(16)=(128)/(16) \\ a=\text{ 8 miles per hour} \end{gathered}`

Therefore the speed of the boat in still water = 8 miles per hour

Step 4

Find the speed of the current of the water.

`\begin{gathered} \text{From 1} \\ 24=2a+2c \\ 24=2(8)\text{ + 2c} \\ 24=16\text{ + 2c} \\ 2c\text{ = 24-16} \\ 2c=\text{ 8} \\ (2c)/(2)=(8)/(2) \\ c=\text{ 4 miles per hour} \end{gathered}`

Hence, the speed of the current of the water = 4 miles per hour