Step 1
Let a = speed of the boat in still water
Let c = Speed of current
Upstream;
[tex]\begin{gathered} speed\text{ = }a-c \\ d_u=(a-c)t_u \end{gathered}[/tex]
Downstream;
[tex]\begin{gathered} \text{Speed}=\text{ a+c } \\ d_d=(a+c)t_d \end{gathered}[/tex]
Step 2
Given that
[tex]\begin{gathered} d_d=24\text{ miles} \\ d_u=\text{ 16 miles} \\ t_u=4\text{ hours} \\ t_d=\text{ 2 hours} \end{gathered}[/tex]
Hence;
[tex]\begin{gathered} 24=(a+c)2----(1) \\ 16=(a-c)4---(2) \\ 24\text{ = 2a+2c} \\ 16=4a-4c \end{gathered}[/tex]
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,
[tex]\begin{gathered} \frac{16a}{16}=\frac{128}{16} \\ a=\text{ 8 miles per hour} \end{gathered}[/tex]
Therefore the speed of the boat in still water = 8 miles per hour
Step 4
Find the speed of the current of the water.
[tex]\begin{gathered} \text{From 1} \\ 24=2a+2c \\ 24=2(8)\text{ + 2c} \\ 24=16\text{ + 2c} \\ 2c\text{ = 24-16} \\ 2c=\text{ 8} \\ \frac{2c}{2}=\frac{8}{2} \\ c=\text{ 4 miles per hour} \end{gathered}[/tex]
Hence, the speed of the current of the water = 4 miles per hour
