Aptitude - Boats and Streams - Discussion

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.

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.

My doubt is:
Is he rowing alternatively first 4 km downstream then 3 km upstream so he will cover 28 km @ 4km/hr and 20 @ 3km/hr (kind of work and time example 2 people working on alternate day with different capacity).

Suppose the time taken in downstream be x hour.
distance of downstream = 4km(given).

So speed in downstream = distance/time = 4/x ------(1)

Now according to question same time he is taking for upstream.
so Speed of upstream = 3/x ----------(2).

Now total time given is 14 hours.

According to question:

Time taken by upstream + time taken in downstream = 14 hours.

48/(3/x)+ 48/(4+x) = 14.
Solving this we get x = 1/2.

Now putting this value in equations 1 and 2 we get;

Speed of upstream = 6 km/h.
Speed of downstream = 8km/h.

Now rate of stream = 1/2(Speed of downstream-Speed of upstream).

i.e 1/2(8-6) = 1km/h.

@Jain.

How come v = (48+48)/14 = 7.
The ans is 6.857.

Have you taken it approximately.

I am not able to understand why x=1/2 and,
Speed downstream = (4/x).
Speed upstream = (3/x).

Can anyone clear my doubt?

Don't break your head.
Just follow this:

Assume that he moves 4 km downstream in x hours.

Then, speed downstream = distancetime=4x km/hr.

Given that he can row 4 km with the stream in the same time as 3 km against the stream.

i.e., speed upstream = 34of speed downstream=> speed upstream = 3x km/hr.

He rows to a place 48 km distant and come back in 14 hours.

=>48/(4x)+48/(3x)=14==>12x+16x=14=>6x+8x=7=>14x=7=>x=12Hence, speed downstream = 4x=4(12) = 8 km/hrspeed upstream = 3x=3(12) = 6 km/hr.

Now we can use the below formula to find the rate of the stream.

At his usual rowing rate rahul can travel 12 mile downstream in a river in six he less than it takes him to travel the same distance upstream. But if he could doubled his usual speed for 24 miles round trip, the downstream 12 miles would then take only one he less than the upstar. 12 miles. Find current rate per hr?

@Usamah.

If the speed downstream is Akm/hr and the speed upstream is Bkm/hr then;
Rate of stream = 1/2(A-B)km/hr.
Therefore;1/2(8-6).
= 1/2(2).
= 1 answer.

Explain me last step. 1/2(8-6) = 1 km/hr which is rate of stream.