Question

A man can row a boat at 8 km/h in still water. If the speed of the water current is 2 km/h and it takes him 2 hours to row to a place and come back, how far off (in km) is the place?

• A. 7.5 km
• B. 6 km
• C. 9.5 km
• D. 10 km

Answer 1

The Correct Option is A

Given:

• Speed of boat in still water = 8 km/h
• Speed of current = 2 km/h
• Total time for round trip = 2 hours

Let the distance to the place be \(d\) km.

Downstream speed (with current):

\[ \text{Speed}_{\text{down}} = \text{Boat speed} + \text{Current speed} = 8 + 2 = 10 \text{ km/h} \]

Upstream speed (against current):

\[ \text{Speed}_{\text{up}} = \text{Boat speed} - \text{Current speed} = 8 - 2 = 6 \text{ km/h} \]

Time calculations:

\[ \text{Time}_{\text{down}} = \frac{d}{10} \text{ hours} \\ \text{Time}_{\text{up}} = \frac{d}{6} \text{ hours} \]

Total time equation:

\[ \frac{d}{10} + \frac{d}{6} = 2 \]

Find a common denominator (30):

\[ \frac{3d}{30} + \frac{5d}{30} = 2 \\ \frac{8d}{30} = 2 \\ 8d = 60 \\ d = \frac{60}{8} = 7.5 \text{ km} \]

The correct answer is option (1) 7.5 km.

Answer 2

Speed downstream = 10 km/h, speed upstream = 6 km/h. 

Total time = $\frac{d}{10} + \frac{d}{6} = 2$ hours. 

Solving for $d$ gives $d = 7.5$ km.