Question

the speed of a boat in still water is 6.5km/hr and the speed of the stream is 1.5km/hr. A man rows the boat downstream for a certain distance and comes back to the starting point. Find the average speed for the whole journey. ​

Answer 1

Given :-

• The speed of a boat in still water is 6.5km/hr.
• The speed of the stream is 1.5km/hr.

To find :-

• The average speed for the whole journey.

Solution :-

The speed of a boat in still water is 6.5km/hr.

The speed of the stream is 1.5km/hr.

Now,

Speed of upstream = Speed of Boat - Speed of stream

So, speed of upstream = 6.5 - 1.5 = 5 km/hr.

Speed of downstream = Speed of Boat + Speed of stream

So, speed of downstream = 6.5 + 1.5 = 8 km/hr.

Let u = 5 km/hr and v = 8 km/hr

And distance covered be 'x' km

Since distance travelled in both the cases are same, so the average speed is given by

$:  \implies \bf \: average \: speed \: = \dfrac{2 \: uv}{u \: + \: v}$

$:  \implies \bf \: average \: speed \: = \dfrac{2 \: \times 8 \times 5}{8 \: + \: 5}$

$:  \implies \bf \: average \: speed \: = \dfrac{80}{13} \:km/hr$