# Ratio of speed of 2 boats is 5 ∶ 3. The faster boat covers a distance of 130 metre in 5 seconds travelling downstream. If it is given that speed of cu

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Ratio of speed of 2 boats is 5 ∶ 3. The faster boat covers a distance of 130 metre in 5 seconds travelling downstream. If it is given that speed of current is 6 m/s then calculate the time taken by the slower boat when it is travelling the same distance upstream.
1. 22 sec
2. $21\frac{2}{3}\;sec$
3. $22\frac{4}{5}\;sec$
4. $19\frac{3}{2}\;sec$
5. None of these

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Correct Answer - Option 2 : $21\frac{2}{3}\;sec$

Given:

Distance travelled by boat = 130 metre

Speed of stream = 6 m/s

Concept used:

If the speed of boat in still water is ‘x’ km/hr and speed of stream is ‘y’ km/hr, then:

Upstream speed = Speed of boat - Speed of stream = (x – y)

Downstream speed = Speed of boat + Speed of stream = (x + y)

Calculations:

Let the speed of boats be 5x and 3x

∴ For faster boat

Downstream speed = Speed of boat + Speed of stream = 5x + 6

⇒ 5x + 6 = (130/5) = 26

⇒ 5x = 20

⇒ x = 4

∴ Speed of Faster boat = 5 × 4 = 20 km/hr

Speed of slower boat = 3 × 4 = 12 km/hr

∴ Time taken by the slower boat to cover 130 m upstream

⇒ Time = Distance/Speed

⇒ Time = 130/(12 – 6)

⇒ Time = 65/3

∴ Time taken by the slower boat = 65/3 $= 21\frac{2}{3}$