Aptitude - Boats and Streams - Discussion

Why the speed of upstream is 15-x and speed of downstream is 15+x?

A little confusion in simplification. How 900 came? Explain.

Speed in still water = 15 km/hr.
Distance traveled in downstream = 30 km.

Time taken in upstream = 4 hr 30 min.
The speed of the stream = ?

Speed = Distance/time.
Distance = 30km.

Speed in upstream = (u-v)km/hr = (15-v)km/hr.

Speed in downstream = (u+v)km/hr = (15+v)km/hr.

Total time = (distance of downstream/speed of downstream) + (distance of upstream/speed of upstream).

(30/(15+v))+(30/(15-v)) = 4 1/2.

(30*30/(15-v)(15+v)) = 4 1/2.

900/(15^2 - v^2) = 4 1/2.

900/(225 - v^2) = 4 1/2.

900 / (225 - v^2) = 9/2.

900 * 2 = 9(225 -v^2).

1800 = 2025 - 9v^2.

9v^2 = 2025 - 1800.

9v^2 = 225.

v^2 = 225/9.

v^2 = 25.

v = 5 Km/hr.

Hai, Mr. Rajesh Kumar, can you explain me in brief?

How it is possible to multiply the speed of upstream and downstream?

Explain briefly.

Hello friends,

In this Speed of the boat in still water is given that is 15Km/s. and here we find speed of stream. take the answer from bottom suppose i take 10 from bottom.

You can see that speed of boat in upstream become15-10=5 and distance of upstream is 30 given. Here you can find out the time in case of upstream time=dist/speed 30/5=6.

Similarly speed in case of downstream 15+10=25. Distance 30 given time you can find that is=30/25=6/5. In question, we have given total time 4hr 30min. We can see that the answer 10 is choosen by me is wrong. Take 5 in place of 10 you get the answer.

I don't really understand this question. Some one should please help me out.

Simply follow formula when only distance the, time t and speed of boat x given.. and asked for speed of stream.... use in formula,

d^2/(x^2-y^2)=t ,

9/2=(225-y^2)/15, ==> y^2=25 , y=5

Here we have been given the speed of the boat is 15 kmph that too in still water and the boat goes and comes back in 4 and half hour and that distance is 30 kms so we have to find the speed of the stream in kmph.
Let us think that the speed of the stream be X then
We know that Speed of the downstream is (u+v) here u is speed of the boat and v is speed of the stream so
Speed of downstream is (15+x)Kmph
Speed of upstream is (15-x)Kmph
We know that
speed in still water is 1/2(a+b) kmph
so
30/(15+x) + 30/(15-x) = 4 1/2

30*30/(15+x)(15-x) = 4 1/2 [Since we know (a+b)(a-b) = (a2 - b2)

900 / 225 - x2 = 9/2

cross multiply the two fractions

then 900 * 2 = 9(225 -x2)

1800 = 2025 - 9x2

9x2 = 2025-1800

9x2 = 225
x2 = 225/9
x2 = 25
x = 5

This is the solution