Question

4. A man can row at 5 km/h in still water. If the velocity
of current is 1 km/h and it takes him 1 hr to row to a
place and come back, how far is the place?
1) 2.5 km 2) 3 km
3) 2.4 km
4) 3.6 km 5) None of these


​

Answer 1

Given that

• Speed of current = 1 km per hour

• Speed of boat = 5 km per hour

• Total time taken = 1 hour

To Find :-

• The distance

Solution :-

• Let distance be 'x' km.

Now,

It is given that

• Speed of current = 1 km per hour

• Speed of boat = 5 km per hour

So,

• Speed of upstream = 5 - 1 = 4 km per hour

and

• Speed of downstream = 5 + 1 = 6 km per hour

Case :- 1

• Speed of upstream = 4 km per hour

• Distance covered in upstream = x km

Let time taken to covered 'x' km at the speed of 4 km per hour is 't' hours.

So,

$\rm :\longmapsto\:t = \dfrac{x}{4} \: hours \: - - - (1)$

Case :- 2

• Speed of downstream = 6 km per hour

• Distance covered in downstream = x km

Let time taken to covered 'x' km at the speed of 6 km per hour is 'T' hours.

So,

$\rm :\longmapsto\:T= \dfrac{x}{6} \: hours \: - - - (2)$

According to statement,

Total time taken = 1 hour.

$\rm :\longmapsto\:t + T = 1$

$\rm :\longmapsto\:\dfrac{x}{4} + \dfrac{x}{6} = 1$

$\rm :\longmapsto\:\dfrac{3x + 2x}{12} = 1$

$\rm :\longmapsto\:\dfrac{5x}{12} = 1$

$\bf\implies \:x = \dfrac{12}{5} = 2.4 \: km$

Hence,

• Option (3) is correct.

Answer 2

$\sf\bold{\underline{Given:}}$

• Man can row in a speed of 5 km/h in still water.
• velocity of current : 1 km/h
• Time taken by man to row to a place and come back = 1 hour.

$\sf\bold{\underline{To\:find:}}$

• Distance of the place.

$\sf\bold{\underline{Solution:}}$

Let the place be at distance of x km.

$\sf\bold{\underline{Condition\: I}}$

when man goes in downstream direction, the velocity of man will increase as we will add velocity of current with velocity of man.

$\sf\longmapsto{5+1=6km/h}$

$\sf\bold{\underline{Condition \:II}}$

when man goes in upstrean direction, the velocity of man will decrease as we will subtract velocity of current from velocity of man.

$\sf\longmapsto{5-1=4km/h}$

Total time taken to row to a place and come back is 1 hour.

It can also be written as,

$\sf\implies{\dfrac{x}{6} + \dfrac{x}{4} = 1}$

$\sf\implies{\dfrac{4x+6x}{24} = 1}$

$\sf\implies{\dfrac{10x}{24} = 1}$

$\sf\implies{x=\dfrac{24}{10} = 2.4km}$

$\sf\therefore{Hence,\:option \:(3)\:2.4\:km\:is\:correct}$

NOTE:-

1. One should be carefull about the unit of distance, as velocity is given in km/h so distance should be in km.

2. Downstream in the river means, we are going with the flow of river so, we will add the velocities

3. Upstream in the river means, we are going in opposite direction of flow of river so, velocities must be subtracted

@BrainlicaLDoll