Aptitude - Boats and Streams - Discussion

On what basis Upstream and down stream speed is calculated?

Speed of boat in still water = 9 kmph.
Speed of stream = 1.5 kmph.

Given distance from boat to a place is 105 km.

Consider a man want to go to that place, means he want go in opposite direction of boat( away from boat).

So we take upstream = sp(boat)-sp(stream) = 9-1.5 => 7.5kmph.
Time taken to travel in upstream is 105/7.5 = 14 hours.

By returning he travel towards boat sp(boat)+sp(stream) = 9+1.5 =>10.5kmph.
Time taken to travel in downstream is 105/10.5 = 10 hours

Total time taken to travel == 14+10 = 24 hours.

How to know downstream and upstream?

How? explain this.

Guys, it's very simple you don't need to find upstream or downstream speed you can the total time like this.

Let T be total time and t1=return time and t2=going time and D = be the distance(105) x=still water speed of man and y=stream speed so,

T = t1+t2
T = (D/x+y)+(D/x-y) {definitely one direction will be upstream n oppsite dir will b downstream}
T = D{(2x)/(x^2 - y^2).

Solution.
T = (105 *2*9)/(9^2-1.5^2).
T = (1890)/(78.75),
T = 24 Hours.

The upstream and downstream speeds are calculated on relative motion.

If two bodies are moving in the same direction their speed is substracted and if they're moving in an opposite direction they are added.

How did we get that once it was upstream and next time it was downstream?

Guys look current or speed of boat mean v and in still water or stationary means u.

So for down u+v and for upstream u-v. So calculate the time by t=d/s and add both the time.

As we know speed of the boat is U and the speed of the stream is V,

For Upstream speed=U-V (9-1.5).
For downstream speed = U+V (9+1.5).
what he mentioned is he rows against the stream with a distance of 105km.
in order to find the total time took i.e., T=D/S.
so, T=105/10.5 + 105/7.5 (downstream) = 24hrs.

U.S = 1/2(P+Q).
D.S = 1/2(P-Q).