Question

The distance between two piers on a river is $45$ miles.

It takes a motorboat, moving down river, $2hr15min$to complete the journey.

How much time does it take the same boat to go back upstream if the current flows at $2.5mph$?

Answer 1

Explanation to correct answer:

Step-1: Speed of the motor boat.

Given,

Distance between rivers = $45$ miles

Speed of current flow of water = $2.5mph$

Time to complete journey = $2hr15min$

We know that

$$\begin{gathered} 60minute=1hour \\ \Rightarrow 1minute=\frac{1}{60}hour \\ \Rightarrow 15minute=\frac{15}{60}hour \\ =\frac{1}{4}hour \end{gathered}$$

Therefore, Time to complete journey is $2+\frac{1}{4}hours$

Let the speed of the motor boat be $xmph$

When moving downriver, the net speed with which the motorboat moves is given as

Speed of the motor boat $+$Sped of downriver$=x+2.5mph$

Now, we know that

Time taken$=\frac{\text{distance}}{\text{speed}}$

$$\begin{gathered} \Rightarrow 2+\frac{1}{4}=\frac{45}{x+2.5}\left[given\right] \\ \Rightarrow \frac{9}{4}=\frac{45}{x+2.5} \\ \Rightarrow 9\left(x+2.5\right)=45\times 4 \\ \Rightarrow 9x+22.5=180 \\ \Rightarrow 9x=180-22.5 \\ \Rightarrow x=\frac{157.5}{9} \\ \Rightarrow x=17.5 \end{gathered}$$

Therefore, the speed of the motorboat is $17.5mph$

Step 2: Find the time to take the same boat to go back upstream.

When moving upstream, the net speed with which the motorboat moves is given as

Speed $=$ Speed of the motor boat $-$Sped of downriver

$$\begin{gathered} =17.5-2.5 \\ =15mph \end{gathered}$$

Time taken

$=\frac{\text{distance}}{\text{speed}}$

$$\begin{gathered} =\frac{45}{15} \\ =3hours \end{gathered}$$

Hence, the time to take the same boat to go back upstream is $3hours$.