Calculating Rowing Speeds: Still Water & Stream

This problem involves calculating the speed of a boat in still water and the speed of the water current using the given upstream and downstream speeds.

Formulas Used

• Let b represent the man's speed in still water (km/h).
• Let w represent the speed of the water current (km/h).
• Downstream Speed = Speed in Still Water + Speed of Water (b + w)
• Upstream Speed = Speed in Still Water - Speed of Water (b - w)

Given Information

• Upstream Speed = 8 km/h
• Downstream Speed = 12 km/h

Setting Up the Equations

Using the formulas, we can set up a system of two linear equations:

1. b + w = 12 (Downstream speed)
2. b - w = 8 (Upstream speed)

Solving for Speeds

To find the speeds, we solve the system of equations:

1. Step 1: Find the speed in still water (b) Add the two equations together:

   $ (b + w) + (b - w) = 12 + 8 $

   $ 2b = 20 $

   $ b = \frac{20}{2} $

   $ b = 10 \text{ km/h} $

   So, the man's speed in still water is 10 km/h.
2. Step 2: Find the speed of the water (w) Substitute the value of b (10 km/h) into the first equation:

   $ 10 + w = 12 $

   $ w = 12 - 10 $

   $ w = 2 \text{ km/h} $

   So, the speed of the water is 2 km/h.

Conclusion

The man's speed in still water is 10 km/h and the speed of the water is 2 km/h. This matches the first option.