Question

A tugboat goes 180 miles upstream in 15 hours. The return trip downstream takes 5 hours. Find the speed of the tugboat without a current and the speed of thecurrent

Answer 1

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:

`Su=(180)/(15)=12\text{mph}`

Step 02: Find the speed downstream.

sd is:

`Sd=(180)/(5)=36\text{mph}`

Step 03: Write an equation for each speed.

Consider:

a = speed of tugboat

b = speed of current

Then,

`\begin{gathered} 12=a-b \\ 36=a+b \end{gathered}`

Step 04: Isolate "a" in the first equation.

To do it, add "b" to both sides.

`\begin{gathered} 12+b=a-b+b \\ 12+b=a \end{gathered}`

Step 05: Substitute a by 12 + b in the second equation.

`\begin{gathered} 36=a+b \\ 36=12+b+b \\ 36=12+2b \end{gathered}`

To isolate b, subtract 12 from both sides, then divide the sides by 2.

`\begin{gathered} 36-12=12+2b-12 \\ 24=2b \\ (24)/(2)=(2)/(2)b \\ 12=b \end{gathered}`

Step 06: Substitute b by 12 in the equation from step 04.

`\begin{gathered} a=12+b \\ a=12+12 \\ a=24 \end{gathered}`

Answer:

The speed of the tugboat is 24 mpf.

The speed of the current is 12 mpf.