Respuesta :
To answer the question, follow the steps below.
Step 01: Find the speed upstream.
The speed is the ratio between the distance (miles) and the time (hours).
So, the speed upstream (su) is:
[tex]Su=\frac{180}{15}=12\text{mph}[/tex]Step 02: Find the speed downstream.
sd is:
[tex]Sd=\frac{180}{5}=36\text{mph}[/tex]Step 03: Write an equation for each speed.
Consider:
a = speed of tugboat
b = speed of current
Then,
[tex]\begin{gathered} 12=a-b \\ 36=a+b \end{gathered}[/tex]Step 04: Isolate "a" in the first equation.
To do it, add "b" to both sides.
[tex]\begin{gathered} 12+b=a-b+b \\ 12+b=a \end{gathered}[/tex]Step 05: Substitute a by 12 + b in the second equation.
[tex]\begin{gathered} 36=a+b \\ 36=12+b+b \\ 36=12+2b \end{gathered}[/tex]To isolate b, subtract 12 from both sides, then divide the sides by 2.
[tex]\begin{gathered} 36-12=12+2b-12 \\ 24=2b \\ \frac{24}{2}=\frac{2}{2}b \\ 12=b \end{gathered}[/tex]Step 06: Substitute b by 12 in the equation from step 04.
[tex]\begin{gathered} a=12+b \\ a=12+12 \\ a=24 \end{gathered}[/tex]Answer:
The speed of the tugboat is 24 mpf.
The speed of the current is 12 mpf.
