Question

A boat takes 8 hours to cover a distance while traveling upstream, whereas while traveling downstream it takes 6 hours. If the speed of the current is 4 kmph, what is the speed of the boat in still water?

• A. 28 kmph
• B. 8 kmph
• C. 32 kmph
• D. 30 kmph
• E. 14 kmph

Hint:

For boat problems, remember: $d = (b \pm (c) \times t$. Set the distances equal to solve for the unknown.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Upstream speed \( = B - C \) and Downstream speed \( = B + C \), where B is boat speed and C is current speed.
Step 2: Key Formula or Approach:
Distance \( D = S \cdot T \). Equate distances for both cases.
Step 3: Detailed Explanation:
Let boat speed be \( B \). Current speed \( C = 4 \).
Upstream distance: \( D = (B - 4) \cdot 8 \).
Downstream distance: \( D = (B + 4) \cdot 6 \).
Equating them:
\( 8B - 32 = 6B + 24 \)
\( 2B = 56 \Rightarrow B = 28 \) kmph.
Step 4: Final Answer:
The speed of the boat in still water is 28 kmph.