Aptitude - Boats and Streams - Discussion

Some body says why = 1/2. Solution is 48/(4/x)+48/(3/x) = 14.
Now 48x/4+48x/3 = 14.

Take x as common x(48/4+48/3) = 14.
Then x(12+16) = 14.

28x = 14.
x = 12.

Hope this method will help you guys.

Speed of boat: B km/h;
Speed of stream: S/km/h;

So Downstream Speed (with the stream) = Speed of boat + Speed of stream;

Upstream Speed (against the stream) = Speed of boat - Speed of stream;

Downstream speed = (B+S) km/h;
Upstream Speed = (B-S) km/h;
Total Distant = 48 km;

Since in question, it is given that time taken by a man to travel 4 km with stream (B+S) is equal to time taken to travel 3 km in against direction (B-S).

Or

4 km with (B+S) km/h = 3 km with (B-S) km/h.

4/(B+S) = 3/(B-S);
4B-4S = 3B+3S;
B = 7S;
B/S = 7/1;

So Boat speed = 7x;
Stream Speed = x;

Now using question first line:

A man rows to a place 48 km distant and come back in 14 hours.
Time taken to travel down stream + time taken to travel upstream = 14;

= 48/(7x+x) + 48/(7x-x) =14;
= 6/x + 8/x = 14;
x = 1;

So boat speed = 7*x = 7*1 = 7km/h;
Stream speed = x = 1 km/h;

Thanks.

Let rate of stream and still water be v km/hr and u km/hr respectively.

So speed in downstream = u+v km/hr.

Speed in upstream = u-v km/hr.

In question distance traveled in both direction is same = 48 Km.

So 4/u+v = 4/u-v.

=> u/v = 7/1.

Now we can say u = 7k & v = k.

So time of downstream = 48/8k = 6/k and time in upstream = 48/6k = 8/k.

Now from question time up + time down = 14hr.

So (8/k)+(6/k) = 14 => k = 1. So u = 7 km/h.

And v = 1 km/h answer.

How did you got that x=12 I think x=7/14 so x=1/2?

Can you explain me is it right are wrong please?

Why we divide this by x?

I think answer should be 2 km/hr.

Downstream 4/x = 4/1/2 = 4*2 = 8kmph.

Upstream 3/x = 3/1/2 = 3*2 = 6kmph.

This can also be solved using Avg speed concept.

Let t be time taken.
Let x be stream speed & v be boat speed.

Total distance = 48 + 48 = 96.
Time = 14 hrs.

So, 96/14 = 2ab/(a+b) = 2((4/t*3/t)).
==> 7/t.

Solving we get t = 1/2 hr.
=> 4/(1/2) = 8.
=> 3/(1/2) = 6.
So, v+x = 8 & v - x =6.
Solving we get v=7 : x=1.
Stream speed = 1/2 (8 - 6) = 1 km/hr.

A man can row 24 km upstream and 54 km downstream in 6 hours. He can also row 36 km upstream and 48 km downstream in 8 hours. What is the speed of the man in still water?