Aptitude - Boats and Streams - Discussion

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.

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.

Upstream speed = 9 - 1.5 = 7.5kmph.

Downstream speed = 9+1.5 = 10.5kmph.

D = S * T
D = 105kmph, S in upstream = 7.5kmph.

T has taken in upstream = 105/7.5.

Similarly,

T has taken in downstream = 105/10.5.

Total time taken = ( 105/7.5.)+ (105/10.5).

Multiply by 10,

T = (105*10/75) + (105*10/105).

T = 14 + 10.

T = 24hrs.

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.

Upstream speed = 9 - 1.5 = 7.5kmph.
Downstream speed = 9+1.5 =10.5kmph.

s = d/t
t = d/s...[in both case of upstream and downstream so addition of both].

t = 105/7.5 + 105/10.5.
Multiply by 10, to remove the denominator point;

t = (105*10/75) + (105*10/105).
t= 14 + 10.
t= 24hrs.

Average speed During the Journey = (2*(9+1.5)*(9-1.5))/(9+1.5)+
(9-1.5)

so,Average speed=8.75 kmph

so,Total time= total distance/average speed
=(105*2)/8.75
= 24 hours.

Guys, It's given the Speed of a boat in standing water and asking for the time taken by man to travel upstream and downstream. How you guys calculate upstream and downstream for the man?

Can't get it, Please explain.

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.

9 km/hr is the speed of boat in standing water.

Boat has to move twice the distance of 105km to reach at same point.

Then (105/9)+(105/9) = 23.33333333333333333.

Then It should be 24hr.

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.