A boat’s speed in still water is 6 km/h and the stream’s speed is 1.5 km/h. The man rows to a place 22.5 km away and returns to the start. Find the total time taken (in hours and minutes).

Difficulty: Easy

Correct Answer: 8 hrs

Explanation:


Introduction / Context:
Compute leg times with effective upstream and downstream speeds and sum them to get the total duration.


Given Data / Assumptions:

  • b = 6 km/h; c = 1.5 km/h
  • Downstream speed vd = 7.5 km/h
  • Upstream speed vu = 4.5 km/h
  • Distance each way = 22.5 km


Concept / Approach:
Total time = 22.5/7.5 + 22.5/4.5 (hours).


Step-by-Step Solution:

Downstream time = 22.5 / 7.5 = 3 hUpstream time = 22.5 / 4.5 = 5 hTotal = 3 + 5 = 8 h


Verification / Alternative check:
All values align with b ± c; no inconsistencies appear.


Why Other Options Are Wrong:
Any other total would not match both leg computations given the fixed speeds and distance.


Common Pitfalls:
Averaging the two speeds to get a single speed for the round trip is invalid; use time per leg instead.


Final Answer:
8 hrs.

More Questions from Boats and Streams

Discussion & Comments

No comments yet. Be the first to comment!
Join Discussion