Question

A motorboat covers a given distance in $6$hour moving downstream on a river. It covers the same distance in$10$ hour moving upstream. The time it takes to cover the same distance in still water is

• A. $9$ hour
• B. $7.5$ hour
• C. $6.5$ hour
• D. $8$ hour

Answer 1

The correct option is B

$7.5$ hour

Explanation for the correct option:

Step 1. Assume the velocity of water and motorboat :

Let, the velocity of water $=w$

and the velocity of the motorboat in still water $=s$

The distance covered by a motorboat in moving downstream in $6$hr is

$=(s+w)\times 6$ (distance = velocity x time)

The same distance covered by the motorboat in moving upstream in $10$hr is

$=(s-w)\times 10$

Step 2. Apply the condition :

$(s+w)\times 6=(s-w)\times 10$

$\Rightarrow$ $6s+6w=10s-10w$

$\Rightarrow$ $16w=4s$

$\Rightarrow$ $w=0.25s$

So, distance $=(s+w)\times 6$

$=(s+\hspace{0.17em}0.25s)\times 6$

$=7.5s$

Step 3. Calculate the time :

The time is taken by the motorboat to cover the same distance in still water

$Time=\frac{Dis\tan ce}{s}$

$=\frac{7.5s}{s}$

$=7.5$ hour

Hence, the correct option is B.