The speed of a boat in still water is 12 km/h, and the speed of the stream is 3 km/h. A man goes to a place by boat, 45 km away, and comes back to the starting point. Find the total time taken by him.
8 hours
To solve this problem, we need to determine the total time taken for the man to travel 45 km upstream and 45 km downstream. Here's how we can calculate it:
The speed of the boat in still water (b) is 12 km/h.
The speed of the stream (s) is 3 km/h.
When the boat is going downstream, the speeds add up: the effective speed downstream (b + s) = 12 km/h + 3 km/h = 15 km/h.
When the boat is going upstream, the speeds subtract: the effective speed upstream (b - s) = 12 km/h - 3 km/h = 9 km/h.
Now, we calculate the time taken for each leg of the journey:
Time taken to travel 45 km downstream = Distance / Speed = 45 km / 15 km/h = 3 hours.
Time taken to travel 45 km upstream = Distance / Speed = 45 km / 9 km/h = 5 hours.
Therefore, the total time taken for the entire journey (to the place and back) is simply the sum of the downstream and upstream times:
Total time = 3 hours (downstream) + 5 hours (upstream) = 8 hours.
Hence, the total time taken by the man is 8 hours.
Important Questions from Boat and River
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