Question

A boat takes $2hr$ to travel $8km$ and back in still water. If the velocity of water is $4km/h$r, the time taken for going upstream $8km$ and coming back is:

• A. $2hr$
• B. $2hr40min$
• C. $1hr20min$
• D. Cannot be estimated with the information given

Answer 1

The correct option is B

$2hr40min$

Step 1: Given data

Distance travelled by boat $=16km$

Time taken by the boat $=2hr$

Water velocity $=4km/hr$

Step 2 : Calculating speed of boat in still water

Speed of boat in still water $=\frac{Dis\tan ce}{Time}$

$$\begin{gathered} =\frac{16}{2} \\ =8km/hr \end{gathered}$$

Step 3 : Calculating velocity and time taken during upstream

Velocity in upstream direction = Velocity of boat - Velocity of water

$$\begin{gathered} =8–4 \\ =4km/hr \end{gathered}$$

Time for travelling $8km$ upstream $=\frac{Dis\tan ce}{Speed}$

$$\begin{gathered} =\frac{8km}{4km/hr} \\ =2hr \end{gathered}$$

Step 4 : Calculating velocity and time taken during downstream

Velocity in downstream direction $=Velocityofboat+Velocityofwater$

$$\begin{gathered} =8km/hr+4km/hr \\ =12km/hr \end{gathered}$$

Time for travelling $8km$ downstream $=\frac{Dis\tan ce}{Speed}$

$$\begin{gathered} =\frac{8km}{12km/hr} \\ =\left(\frac{2}{3}\right)hr \\ =\frac{2}{3}\times 60min \\ =40min \end{gathered}$$

Total time of travelling = Time for travelling $8km$ upstream $+$ Time for travelling $8km$ downstream

$$\begin{gathered} =2hr+40min \\ =2hr40min \end{gathered}$$

Hence, option (B) is correct.