Aptitude - Boats and Streams - Discussion

Please explain in detail.

Why we not take ?

3/x+3 + 3/x-3 = 5/2 ( total hrs = 1 hrs + 1 1/2 hrs)

SHORT-CUT

90-60=30/2=15KMH

Assume, Let the speed of the boat in still water be x kmph, Then
Speed downstream = (x + 3) kmph,
Speed upstream = (x - 3) kmph.
Given Time of downstream has 1 hour and while it comes back in
1(1/2) hours.i.e 1+(1/2)=3/2 hour ( Taking LCM)
we need to find out distance, Distance=velocity*Time
By Equating on both side,
Velocity of downstream * Time taken by downstream = Velocity of Upstream * Time taken by Upstream

(x + 3) x 1 = (x - 3)x 3/2
(x + 3) = (3x-9)/2
2(x+3) = (3x-9)
2x+6 = 3x-9
3x-2x = 6+9
x=15 km

D1 = D2.
SO, U = X.

A = X+3, B = X-3.
A*T1 = B*T2.

HERE, T1 = 1, T2 = 3/2.

THEREFORE,
X=U=15KMPH.

@Rehman how you can do in short cut way?

Why don't we take that 1 as upstream and 3/2 as downstream because they mention that boat covers a certain distance but not downstream are upstream please help me to understand.

Suppose we assuming the distance D;

So the speed downstream = X+Y = D/1;

Therefor X+Y = D;.....1.

And the speed upstream = X-Y = 2D/3;

(3X- 3Y)/3 = D......2.

If we compare both equations and take Y = 3 kmph as given;

We will get X = 15 kmph which is the speed of still water.

It has a simple formula. A man rows certain distance downstream in x hrs and returns the same distance in y hrs . when to stream flows at a rate of a km/hr then,

Speed of boat or man in still water = a(x + y)/(y - x),

That is speed of boat in still water = 3(1 + 1.5)/(1.5 - 1) = 15 km/hr.

You can also find the speed of stream when the boat is traveling with b km/hr = b(y - x)/(x + y).

Is there any shortcut way?