Question

pratik takes 12 hours to travels 36 km downstream and returns to same spot the speed of the boat in still water is 8 km per hour . find the speed of water current​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

The speed of water current = 4 km/h

Step-by-step explanation:

Given:

• Pratik takes 12 hours to travels 36 km downstream and returns to same spot.
• The speed of the boat in still water is 8 km per hour.

To find:

• The speed of water current.

Solution:

Let the speed of water current be x.

Speed of of the boat in still water = 8 km/h

In downstream, the speed of water current increases the speed of the boat, whereas upstream, the speed of water current decreases the speed of the boat.

Therefore,

• The speed of the boat in upstream = 8 - x km/h
• The speed of the boat in downstream = 8 + x km/h

Now,

• Time taken to cover 36 km upstream = Distance/Speed
• Time taken to cover 36 km upstream = 36/(8 - x)

• Time taken to cover 36 km downstream = Distance/Speed
• Time taken to cover 36 km downstream = 36/(8 + x)

According to the problem,

• 36/(8 - x) + 36/(8 + x) = 12
• 36 [1/(8 - x) + 1/(8 + x)] = 12
• 1/(8 - x) + 1/(8 + x) = 12/36
• 1/(8 - x) + 1/(8 + x) = 1/3
• ((8 + x) + (8 - x))/(( 8 - x) + (8 + x)) = 1/3
• 16/(8² - x²) = 1/3
• 16/(64 - x²) = 1/3
• 3 × 16 = 64 - x²
• 48 + x² = 64
• x² = 64 - 48
• x² = 16
• x = ±√16

Take positive

• x = 4

Therefore,

The speed of water current = 4 km/h

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