Aptitude - Boats and Streams - Discussion

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

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 + x) + 30/(15 - x) = 4 1/2,
30/(15 + x) + 30/(15 - x) = 9/2,
30(15 - x) + 30(15 + x) = 9/2 * (15 - x)(15 + x),
900 = 9/2 * (225 + 15x - 15x - x^ 2),
900 = 9/2 * (225 - x ^ 2),
1800= 9(225 - x ^ 2),
1800 = 2025 - 9x ^ 2,
2025 - 1800 = 9x ^ 2,
225 = 9x ^ 2,
x ^ 2 = 225/9 = 25,
x = √(25) = 5.
Ans=>X=5.

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(1/(15-v))+(1/(15+v)) = 4 1/2.
(30((15+v)+(15-v))/(15+v)(15-v))=9/2
(30(15+15+v-v)/(15^2-v^2))
30*30/225-v2=9/2
900/(225 - v^2) = 9/2
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.

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.

See its simple to understand.

Given distance is 30km. Let assume speed of river is x.

Speed of boat is 15 once it goes downstream. So speed would be 15+x.

And upstream is 15-x.

Now what it told from going to 30 km time required would be 30/downstream and coming back speed would be 30/upstream.

So total time given here is 4.30 minutes which is 4*1/2 (1/2 here means 30 minutes which is half of 1 hr).

So adding both the times downstream and upstream would give total time which is 4*1/2.

i.e why its gives 30/(downstream speed)+30/(upstream) = 4*1/2.

And now you are smart enough to solve equations.

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.

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

Don't multiply take LCM then it will be;

{ 30(15- x)+30(15+x)}/(15+x)(15-x) = 4 1/2.
450-30x+450+30x /(15+x) (15 - x) = 9/2.
-30x+30x will be cancelled then;
900 /15^2-x^2=9/2.
**(a+b)(a-b)=a^2-b^2 **

When cross multiplied we get;
2 * 900=9(15^2-x^2),
1800=2025-9x^2 so,
9x^2=2025-1800,
9x^2=225,
x^2=225/9,
x^2=25,
x = 5.

As we have given upstream speed=15 from option lets take 4 so for,

Downstream 15 + 4 = 19 and upstream 15 -4 = 11.

The distance is given so 30/19=1.58 and 30/11=2.72 it not satisfy condition so take next option
as 5 so similarly 15 +5 = 20 and 15 - 5 =10 so 30/20 = 1.5 and 30/10 = 4.

So 1.5 +4 = 4.5 and our time is also 4.5 so the answer is 4.5.

Speed= 15km/hr
Distance= 30 km/hr
Time= distance/speed
Speed of stream (v) is taken as x
Speed of boat in still water(u)=15km/hr
So,
Speed upstream=(15-x) km/hr.
Speed downstream=(15+x)km/hr.

30/15+x + 30/15-x=4 1/2(this is equation is written with the help of, time= distance/speed)
Further calculations are made. So we get x=5 km/hr.

Actually all of them are wrong who are saying that the answer would be 5.

Because the first step itself is wrong.

If a man covers a certain distance at x km/hr and returns at y km/hr then the avg speed is 2xy/(x+y). I think you all know this.

So the first step will be,

2(15+x)(15-x)/(225-x2) = (30)/(4.5).

Guys think about it.