Question

A raft was sent away from point $\mathrm{A}$ downstream.

A patrol boat left $\mathrm{A}$ $5$ hour and $20$ min later and caught up with the raft $20\mathrm{km}$ away from point $\mathrm{A}$.

What was the speed of the raft if the speed of the patrol-boat was $12\mathrm{km}/\mathrm{hour}$?

Answer 1

Find the speed of the raft if the speed of the patrol-boat was $\mathbf{12}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{hour}$:

Given that,

A raft was sent away from point $\mathrm{A}$ downstream.

A patrol boat left $\mathrm{A}$, $5$ hour and $20$ min later, and caught up with the raft $20\mathrm{km}$ away from the point $\mathrm{A}$.

So, the total distance covered by raft $\mathrm{d}=20\mathrm{km}$

Use the speed formula $\mathrm{s}=\frac{\mathrm{d}}{\mathrm{t}}$.

Where $\mathrm{s}$ is the speed, $\mathrm{d}$ is the distance and $\mathrm{t}$ is the time.

To calculate time $\mathrm{t}=\frac{\mathrm{d}}{\mathrm{s}}$.

Step-1: Find the time the patrol boat takes to travel.

Patrol Boat takes $5$ hour and $20$ min.

So the time take by it is:

$\begin{array}{rcl}& \Rightarrow & \mathrm{t}=5+\frac{20}{60}\left[\mathrm{To}\mathrm{convert}\mathrm{into}\mathrm{hours},\mathrm{divide}\mathrm{minutes}\mathrm{with}\mathrm{hours}\right]\\ & \Rightarrow & \mathrm{t}=5+0.\overline{3}\\ & \Rightarrow & \mathrm{t}=5.\overline{3}\mathrm{hrs}\end{array}$

Also, the patrol boat caught up with the raft $20$ kilometers away from point $\mathrm{A}$ at a speed of $12\mathrm{km}/\mathrm{hr}$.

Calculate the time that will be taken by the patrol boat to reach the raft.

So, substitute $\mathrm{d}=20$ and $\mathrm{s}=12$ into the formula $\mathrm{t}=\frac{\mathrm{s}}{\mathrm{d}}$:

$\begin{array}{rcl}& \Rightarrow & \mathrm{t}=\frac{20}{12}\\ & \Rightarrow & \mathrm{t}=1.\overline{6}\mathrm{hrs}\end{array}$

So, the total time taken by the patrol boat to reach the raft is:

$\begin{array}{rcl}& \Rightarrow & \mathrm{t}=5.3333+1.6666\\ & \Rightarrow & \mathrm{t}=6.9993\\ & \Rightarrow & \mathrm{t}\approx 7\mathrm{hrs}\end{array}$

Step-2: Find the speed of the raft if the speed of the patrol-boat was $\mathbf{12}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{hour}$.

So, the raft traveled a total of $20\mathrm{km}$ from $\mathrm{A}$ and takes $7\mathrm{hrs}.$

Substitute $\mathrm{d}=20\mathrm{km}$ and $\mathrm{t}=7\mathrm{hrs}$ in the speed formula $\mathrm{s}=\frac{\mathrm{d}}{\mathrm{t}}$:

$$\begin{gathered} \begin{array}{rcl}& \Rightarrow & \mathrm{s}=\frac{20}{7}\\ & \Rightarrow & \mathrm{s}=2.\overline{857142}\end{array} \\ \Rightarrow \mathrm{s}\approx 3\mathrm{km}/\mathrm{hr} \end{gathered}$$

Hence, the speed of the raft if the speed of the patrol boat is$\mathbf{12}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{hour}$ is $\mathbf{3}\mathbf{}\mathbf{km}\mathbf{/}\mathbf{hour}.$