Aptitude - Boats and Streams - Discussion

@All.

Against the current - upstream.
Along the current - downstream.

If they mentioned the question like "the speed of the man is...", definitely the answer will be 12.5 km/hr, ie. upstream = speed of the man - speed of the current = 15-2.5=12.5 km/hr.

But,
The question was like "Speed of the man with the current".

ie., 15km/hr is the summation of the speed of the man and the current. so we need to subtract the speed of the current from 15, to know man's speed in water.
ie., 15 - 2.5 = 12.5 => man's speed.
After the above step, we can easily find the man's speed against the current by using the formula below:
upstream = speed of the man - speed of the current.
= 12.5 - 2.5 = 10 km/hr.

Let me explain:

First of all the problem has the data,
speed of man is with current i.e., 15km/hr.
here we can compare it with down stream i.e., speed of boat with the stream.
if we want to take man's speed only we got to substract the speed of current i.e., 2.5 km/hr.
therefore, 15-2.5 = 12.5 km/hr, which is actually man's speed.

In the question they asked us to determine the speed of the man against the current. Here we will compare it with up stream.
i.e. speed of boat against the stream.
there fore, speed of man - speed of current
=12.5-2.5=10km/hr

A man speed with the current means A man moving along with water, means it is downstream(d) speed = 15 km/hrs.

Rate of current or stream (s) = 2.5 km/hrs.

So,

From the downstream formula (d) = b + s.

We know the d and s values, so substitute those values in the above formula and obtain the b value i.e.

b = 15-2.5 ==> 12.5 kh/hrs.

So we need to calculate the man's speed against the water it will happen in upper stream (u) = b - s.

=> 12.5-2.5 ==> 10 km/hrs.

Given:

Speed downstream, a = 15 km/h.
Rate of current, v = 2.5 km/h.

We need to find the value of b, i.e. speed upstream (Speed against the current).

As we know that, speed downstream, a = u+v.
Substituting the value of a and v;

15 = u+2.5.
u = 12.5 km/h.

Now as u = 12.5 km/h and v = 2.5 km/h.
So, speed upstream, b = u-v.

b = 12.5-2.5.
b = 10 km/h answer.

So the right answer is 10 km/h.

Sir, I have one doubt.

Given downstream speed (i.e speed of boat with stream)is 15 km/hr .asked ..upstream speed is( boat speed(u)- stream speed(v)).

Here to find the boat speed we use boat speed= downstream speed - stream speed.what should we do if upstream speed( speed of boat against stream) is given in the question.

Should we do like this, boat speed=upstream speed+ stream speed.

@All.

Suppose you are riding a boat which is arriving to the beach. Naturally, the waves are in the same direction of your boat. Dont you feel easy to drive it then. Hence, the speed of waves/current supplement your boat speed. Then, it is called going downstream or going with the waves/current. Hence, By thinking vice-versa we know that we'd have to subtract the speed of the stream

Why was the speed subtracted. I think it should be added.

For downstream. If we consider velocity of man and velocity of water as vector quantities.

Then velocity of man we are at the stream i.e Stream = Velocity of man we are at ground - Velocity of stream we are at ground.

15 I = x - 2.5 I.

x = 17.5 I.

Can anyone explain my doubt?

This is for @Vijaya.

Suppose there is a river which is flowing from left to right. And if you are swimming left to right. Your speed + River's speed i.e. downstream (with stream).

And if you are swimming from right to left. Your speed - Speed of river upstream (against the river i.e since you are swimming against the upstream speed.

Man's speed with the current means downstream speed i.e. 15 km/ph.

The speed of current means speed of stream i.e 2.5 km/ph.

Man's speed against the current means upstream.

Now we have to find upstream speed.

Speed in current = 1/2 (downstream speed - upstream speed).

2.5 = 1/2 (15 - x).

5 = 15 - x.

-10 = -x.

x = 10 km/ph.

Here time has given 8hr 48min upstream, 4 hours downstream.

T=8 4/5 (While changing min to hours 48/60=4/5)

Upstream speed = Distance/time.
x-y = D/8.4/5.
D = 44/5(x-y)-------> (1)

Now downstream speed=Distance/time.
X+y=D/4,
D=4(X+y) -----------> (2)

Equate eq 1 and 2.
44/5(x-y) = 4(X+y).
24x = 64y.
X/y = 64/24,
X/y = 8:3.