A man can row aboat at 8km/h in still water. If the speed of thewater currentis 2km/h and it takes him 2 hours to row to a place and comeback,how far off (inkm) is the place?

The correct option is 7.5.

To find how far off the place is, we can break down the problem by calculating the speeds of rowing downstream (with the water current) and upstream (against the water current).

Let the speed of the man in still water be represented by $x$ and the speed of the water current be represented by $y$.

Given values:
$x=8\text{km/h}$
$y=2\text{km/h}$

When rowing downstream (in the direction of the water current), the effective speed is the sum of the speed in still water and the current's speed:

$\text{Downstream Speed}=x+y=8+2=10\text{km/h}$

When rowing upstream (against the water current), the effective speed is the difference between the speed in still water and the current's speed:

$\text{Upstream Speed}=x-y=8-2=6\text{km/h}$

Let the distance to the place be $d$ km.

The time taken to travel a distance is given by the formula:

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

Therefore, the time taken to row downstream and upstream can be written as:

$\text{Time taken downstream}=\frac{d}{10}\text{hours}$

$\text{Time taken upstream}=\frac{d}{6}\text{hours}$

According to the problem, the total time for the round trip is 2 hours. This gives us the equation:

$\frac{d}{10}+\frac{d}{6}=2$

To solve for $d$, we find a common denominator for 10 and 6, which is 30, and rewrite the equation:

$\frac{3d}{30}+\frac{5d}{30}=2$

Combining the terms on the left side:

$\frac{8d}{30}=2$

Multiplying both sides by 30:

$8d=60$

Dividing by 8 gives the distance:

$d=\frac{60}{8}=7.5\text{km}$

Thus, the place is 7.5 km away.