Aptitude - Boats and Streams - Discussion

Let me explain.

Ratio between the speed of the boat and speed of the water current is :

Average speed of upstream and downstream to the water current speed (downstream - upward stream velocity we get average water moving velocity).

Does anyone have an easy way to solve the problem?

8 hours 48 minutes is equal to 8.8 hours but how will it be equal to 6.4 hours?

Let me do according to concept wise,

Given upstream time = 8+48/60 = 44/5.
Given downstream time is 4 hr.
We know distance covered by upstream = distance covered by downstream.
Therefore, 44/5(x - y) = 4(x + y).
When you solve the above equation,
we get 24x = 64y.
i.e,x/y = 64/24 = 8/3 the ratio is 8:3 which is the answer.

Given explanation is quite difficult to understand. Let me explain you this in a simpler manner.

Distance is same during upstream and Downstream and Distance is equal to : Speed/Time.

So, time in downstream = 4 hours,
Time in upstream = 44/5 hours (8 hours 48mins).
Now let's assume x as the distance.
A as the downstream speed and B as the upstream speed.

Now write both (as the distance formula),

44/5 = x/B ---> equation 1.
4 = x/A ---> equation 2.

Solving these two equations we get,

44/20 = a/b ---> equation 3.

By equation 3, we can say that a = 44b/20

And we want to calculate u : v.
i.e 1/2(a + b) : 1/2(a - b),
i.e (a + b) : (a - b),
i.e 44b/20 + b : 44b/20 - b,
i.e 64b/20 : 24b/20,
i.e 64b : 24b,
i.e 8 : 3.

That's It. I know it's a bit lengthy But you would be able to calculate 3/4 of these steps orally.

Here distance is constant so, speed inversely proportional to the time.
Time taken by the boat upstream : time taken by the boat downstream = 44/5 : 4
= 11:5.

Speed of upstream : Speed of downstream = 1/11 : 1/5 = 5 : 11.

Speed of boat in still water: speed Of stream= (speed of upstream+speed of downstream) /2 : (speed of upstream speed of downstream)/2.

Therefore, (11 + 5)/2 : (11 - 6)/2 = 16/2 : 6/2.
ie 8:3.

You are right @Bindu.

Let x = speed of boat.
y = speed of stream.
t1= upstream time & t2 = downstrem time.

formula : x/y = (t1 + t2)/(t1 - t2).
{t1 = 8h 48m = 44/5h, t2 = 4h}
so, x/y = (44/5 + 4)/(44/5 - 4).

x/y = (44 + 20)/(44 - 20) = 64/24 = 8/3.

x:y = 8:3.

But I got the answer 3:1.

Please help me to get the correct answer.

Required ratio =(x+y)/2 : (x-y)/2 // here 2 is to take average.

Please, Explain this.