Question

A man rows a boat at a speed of 5km/hr in still water. Find the speed of a river if it takes him 1 hour

to row a boat to a place 2.4 km away and return back.
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Answer 1

Answer:

Speed of man's boat in still water = 5 kmph. Effective speed of man's boat when rowing upstream (against the direction of flow of stream) = (5-1) kmph = 4 kmph. Total time taken is 75 minutes i.e. 1 hour 15 minutes.

Answer 2

The speed of a river is 1 km/hr.

Step-by-step explanation:

Given:

In still water a man rows a boat at a speed of 5 km/hr.

It takes him one hr. to row a boat to a place 2.4 km away and return back.

To Find :

The speed of a river.

Formula Used:

Upstream  speed of boat  = (p−q) km/hr, where  p is the speed of the boat in still water and q is the speed of the stream           ---------formula no.01

Downstream speed of boat  = (p+q)Km/hr, where  p is the speed of the boat in still water and  q is the speed of the stream.       ----- formula no.02

Solution:

As given- in still water a man rows a boat at a speed of 5 km/hr.

 P= 5 km/hr

Applying formula no. 01.

Upstream  speed of boat  $=p-q=5-q$

Applying formula no. 02.

Downstream speed of boat  $=p+q=5+q$

As given - it takes him  one hr. to row a boat to a place 2.4 km away and return back.

$\frac{2.4}{(5+q)} +\frac{2.4}{(5-q)} =1$

$\frac{2.4(5-q)+2.4(5+q)}{(p+q)(p-q)} =1$

$2.4\times10 =5^{2} -q^{2}$

$q^{2} = 25-24$

$q^{2} =1$

$q= 1 and -1$

Considering  + ve value for speed of river.

$q=1km/hr$

The speed of a river is 1 km/hr.

Thus, The speed of a river is 1 km/hr.