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: Define Variables:
Let the speed of the boat in still water be $b$ kmph. Speed of current = $c = 4$ kmph. Upstream speed = $b - c = b-4$ kmph. Downstream speed = $b + c = b+4$ kmph. Let the distance be $d$ km.
Step 2: Form Equations:
Time upstream = $\frac{d}{b-4} = 8$. (1) Time downstream = $\frac{d}{b+4} = 6$. (2)
Step 3: Equate Distance:
From (1): $d = 8(b-4)$. From (2): $d = 6(b+4)$. Thus, $8(b-4) = 6(b+4)$. $8b - 32 = 6b + 24$. $2b = 56 \implies b = 28$.
Step 4: Final Answer:
The speed of the boat in still water is 28 kmph.