Aptitude - Boats and Streams - Discussion

The speed of the boat in still water = Vb.
The speed of stream = Vs.

Question asked -- ratio, Vb : Vs = ?..

Vb + Vs = Vr1 (resultant speed downstream), and time taken to cover a distance "d" with speed Vr1 is 4 hrs.

Similarly,
Vb - Vs = Vr2 (resultant speed upstream), and time is taken to cover the same distance with speed Vr2 is 8 hrs, 48min.
By adding both the equations , we get
2Vb =Vr1 + Vr2.
Vb = (Vr1 + Vr2) 1/2.

lets find Vr1, which is distance d / time taken during upstream i.e Vr1 = d/4,
Similarly, Vr2 = d/(8 + 4/5),
= 5d/44.

in 60 min it is 1 hr so, in 1 min it is 1/60 hrs and in 48 min it is 1/60 * 48 = 4/5 hrs }
Putting Vr1 and Vr2 values in eq 3, we get -
Vb = 2d/11.

Putting value of Vb in eq 1 we'll get;
Vs = 3d/44.

Therefore, Vb/Vs = 8/3 Ans.

Thanks @Bindu.

Let the speed of the boat is u and that of the stream is v.
Time for upstream (u-v) is 528min and time took for downstream (u+v) is 240 min.
Distance covered is the same.

Since, D1=t1*(u-v) and d2= t2*(u+v).
And, d1=d2
So, t1*(u-v) = t2*(u+v).
(U-v)*528 = (u+v)*240
=> u/v = 8/3;
That is 8:3.

An easy way to solve.

Let the speed of boat and water be x km/hr and y km/hr respectively.

Upstream = x-y km/hr.
Downstream = x+y km/hr.

[8+(48/60)](x-y) = 4(x+y)(SINCE DISTANCE IS EQUAL).
8+4/5(x-y) = 4x + 4y.
44/5 x - 44/5 y= 4x + 4y.
44/5x - 4x = 4y + 44/5 y.
24x = 64 y.
x/y = 64/24.
x/y = 16 / 6.
x/y = 8/3 (answer).

If distance is equal thn formula
downstream X time 1 = upstream X time 2

downstream = U+V/2
upstream = U-V/2

downstream = speed of boat
upstream = speed of stream

i.e, U+V/2 * time 1 = U-V/2 * time 2

Now substitute the values in the above formula

Given data,

Upstream time=8 hr 48 min=8x48/60hr=44/5 hr....(1).
Downstream time =4 hr......(2).
The distance is the same.

According to (1) case:
Distance =upstream speed x upstram time.
Distance =(u-v)x44/5=44/5u-44/5v.......(3)

According to (2) case:
Distance =downstream speedxdownstream time
Distance =(u+v)x4=4u+4v........(4)

As distance traveled is equal ,
So (3) =(4).
44/5u-44/5v=4u+4v.
44/5u-4u=4v+44/5v.
24/5u=64/5v.
u/v=8/3.

Thanks @Ajit.

Thanks @Ajit.

Upstream, x = b(speed of boat) - w(speed of water).
Downstream, y = b + w.

Equalling both using distance.
(b+w) *44/5 = (b-w) * 4.
(b+w)*11/5 = (b-w),
11b+11w = 5b-5w.

6b = -16w(ignore negative sign).
b/w = 8/3.
So, b : w = 8 : 3.

8*4/5 will give 44/5 only which is not equal to 8hr 48min.

Please someone explain it to me, how 8hr 48min, how it becomes 8*4/5?