Aptitude - Boats and Streams - Discussion

I have one more way to solve it...

The boat goes downstream in 1 hour and returns back in 3/2 hours so we can conclude the boat covered the same distance.

Now, Sb = 1/2(Sd+Su)
Sb = 1/2(D/1 +D*2/3). As speed = Dist./Time
Sb = D(1/2+1/3)
Sb = D((5/6) -------> (1)

Also, Ss = 1/2(Sd-Su)
Ss = 1/2(D/1-D*2/3)
Ss = D(1/2-1/3)
Ss = D(1/6) -------> (2)

Now if we take ratio of (1) & (2) then,
Sb/Ss = [D(5/6)]/[D(1/6)].
Sb/3 = 5.
As speed of stream is 3kmph.
Sb = 15 kmph.

Here Sb is the speed of the boat.
Ss is the speed of the stream.
Sd is the speed of downstream.
Su is the speed of upstream.
D is distance.

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

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).

If Time=Distance/Speed.

Speed=Distance*Time.

According to condition distance of D.S and U.S is same.
D.S=U.S.
(x+3)*1=(x-3)*3/2 {Remember S=D*T.}.
{i.e D.S and U.S distance which is x+3 and x-3 respectively} and {D.S and U.S time which is 1 and 1*1/2=3/2 respectively}

2x+6=3x-9 (Multiply both equations by 2 to get rid of denominator 2 and solve).
6+9=3x-2x.
x=15.

@All.

By checking the options we can find the answer.

Time has already been given in the question. And these options are the speed of the boat in still water.

And you know the rate of current as well. Just check which option gives you the same distance upstream as well as downstream (D=S*T).

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.

The ratio between time in downstream to upstream is 1:3/2 = 2:3, then the ratio between speed is 2 : 3(directly proportional).
The difference between the ratio is 1 and is given as 3.
The speed of still water is x+y that is (2+3)×3 = 15.

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.

Yes, you are right. @Syed.

But we find only the distance. But the question asked is the speed of the boat in still water.

Can anyone explain this?

But in question, there is still water mention not, the velocity of the boat in "still water" needs to be found not in downstream.