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The speed of a boat along the stream is 8 km/h and against the stream is 6 km/hr. The time taken by the boat to sail 28 km in still water is
  • a)
    2 hrs
  • b)
    3 hrs
  • c)
    4 hrs
  • d)
    8 hrs
  • e)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The speed of a boat along the stream is 8 km/h and against the stream ...
Given, Speed downstream = 8 km/h Speed upstream = 6 km/h 
∴   Speed of boat in still water



Hence, option C is correct.
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Community Answer
The speed of a boat along the stream is 8 km/h and against the stream ...
To solve this problem, we can use the concept of relative speed.

Given:
Speed of the boat along the stream = 8 km/h
Speed of the boat against the stream = 6 km/h
Distance to be covered = 28 km

Let's assume the speed of the stream is x km/h.

The speed of the boat in still water can be calculated using the formula:
Speed of the boat in still water = (Speed along the stream + Speed against the stream) / 2

So, the speed of the boat in still water is:
(8 km/h + 6 km/h) / 2 = 14 km/h

Let's consider two cases:
1. Boat is moving along the stream:
In this case, the effective speed of the boat will be the sum of the speed of the boat in still water and the speed of the stream.
So, the effective speed = 14 km/h + x km/h

2. Boat is moving against the stream:
In this case, the effective speed of the boat will be the difference between the speed of the boat in still water and the speed of the stream.
So, the effective speed = 14 km/h - x km/h

We know that Time = Distance / Speed

1. Time taken to travel 28 km along the stream:
Time = 28 km / (14 km/h + x km/h) = 28 / (14 + x) hours

2. Time taken to travel 28 km against the stream:
Time = 28 km / (14 km/h - x km/h) = 28 / (14 - x) hours

Since the boat is traveling the same distance, we can equate these two times:
28 / (14 + x) = 28 / (14 - x)

Cross-multiplying, we get:
28(14 - x) = 28(14 + x)

Simplifying, we get:
196 - 28x = 392 + 28x

Bringing like terms to one side, we get:
56x = 196

Dividing both sides by 56, we get:
x = 196 / 56 = 7/2 = 3.5 km/h

Now, let's find the time taken to sail 28 km in still water:
Time = 28 km / (14 km/h) = 2 hours

Therefore, the boat takes 2 hours to sail 28 km in still water.
Hence, the correct answer is option (c) 4 hrs.
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