Aptitude - Boats and Streams - Discussion

Easy way to solve this type of question is followed by a simple formula.
i.e
D = T[sb square - ss square]/2*sb.

sb means the speed of a boat.
ss means the speed of a stream.

Why do we need to calculate the downstream and upstream when we already the have speeds of boat(u) and speed of stream(v)? We can directly calculate the time from that.

Like-
u=5
v=1
t=1

Let the distance be x.
So x/5+x/1=1.
Solving the equation we will get the value of x which is 5/6.(but incorrect value).

For Who don't understand how come 12, please refer the following.

x/6 + x/4 = 1
then cross multiply we get;
4x+6x/24 = 1,
24 move to another side we get ;
4x+6x = 24,
divided by 2 for simplify we get;
2x+3x = 12.

Hi friends, in the above explanations we have taken;

time = Distance/Speed
If we take,
distance = speed * time, then;
d=[(u+v)+(u-v)]t.

So, it becomes 10km. This will be the total distance covered by man(including coming back.)
if we want only the distance to a place then it will be 5km.

Why should we not consider this format? can anyone tell me?

Let the distance be X in km.

And speed formula is given by;
speed(or velocity)=distance/time taken.
Speed Upstream= (5-1)=4 kmph.
Speed downstream =(5+1)=6 kmph.
( given time taken to come back is 1hr.)

*Equating time take during Upstream and downstream to 1hour. ie
Time(up strm) +Time(dwn strm) =1---> Eq(1)
(time=distance *speed) so Eq(1)becomes.
X/6 + X/4 =1.
Taking lcm of 6&4 we get 12.
3x+2x=12.
5x=12.
So x=2.4km.

I think you guys got it. Correct me if I have done wrong.

How 2x+3x=12 comes?

Speed downstream = (5 + 1) kmph = 6 kmph.
Speed upstream = (5 - 1) kmph = 4 kmph.

T = 1hr.
total time = (downstream speed/speed of downstream)+(distance of upstream/speed of Upstream).

we don't know distance so let it be 'x'
so, 1 = x/6 + x/4.
take lcm and do eqaution u will get
2x + 3x = 12,
5x = 12,
x = 2.4 km.

I solve this question and I got a different answer i.e. 10 km is the distance.

Upstream speed = 5km/h - 1km/h = 4.
Downstream speed = 5km/h + 1km/h = 6.

Distance =( upstream Speed * time) + (downstream speed * time).
= 4 * 1 + 6 * 1.
=. 10.

@Bhima,

You need to find out the L.C.M of the denominators. We multiply the denominator when L.C.M is not possible.

@Bhima,

You need to find out the L.C.M of the denominators. We multiply the denominator when L.C.M is not possible.