Aptitude - Boats and Streams - Discussion

If the speed downstream is a km/hr and the speed upstream is b km/hr, then:

Speed in still water = (a+b)/2 km/hr.

Rate of stream = (a-b)/2 km/hr.

Given x+y = 8 hours 48 minutes = 44/5.

x-y = 4.

Speed of boat is ((44/5)+4)/2 = 8.

Speed of current is ((44/5)-4)/2 = 3.

So the answer is 8:3.

I don't understand (x*8 4) = (y*4)5.

Speed of the boat upstream = Speed of boat - Speed of stream.

Speed of stream = Speed of boat - Speed of the boat upstream--------- (1).

Speed of the boat downstream = Speed of boat + Speed of stream.

Speed of stream = Speed of the boat downstream - Speed of boat-------- (2).

Now, equating (1) & (2),

Speed of boat-speed of boat upstream = Speed of boat downstream - Speed of boat.

2 (Speed of boat) = Speed upstream + Speed downstream.

Speed of boat = (Speed upstream + Speed downstream)/2.

If, Speed upstream = x and Speed downstream = y then,

Speed of boat = (x+y)/2.

Similarly, making speed of the boat as subject in eq (1) & (2) and then equating we get,

Speed of stream = (Speed downstream - Speed upstream)/2.

= (y-x) /2.

Let as assume,

The speed of boat is : b km/hr.

The speed of the water is : w km/hr.

In downstream the relative speed of the boat is: d = (b + w) km/hr.

In upstream the relative speed of the boat is : u = (b - w) km/hr.

According to the question,

The distance covered in upstream = (b + w) *4 km.

The distance covered in downstream = (b - w) * (8 + 48/60) km.

As the distance covered by boat is same in both direction, Hence.

(b + w) *4 = (b - w) *8.8.

(b*8.8) - (b*4) = (w*4 + w*8.8).

b*4.8 = w*12.8.

b/w = 8/3.

Or b:w = 8:3.

Assume speed of boat = x km/h.
Speed of current = y km/hr.
Downstream speed = u km/h = 4km/h.
Upstream speed = v km/h = 8 hr 48 mins.
=> 8 * 4/5 = 44/5 km/hr.

Speed = Distance/Time.
So,
Distance = speed * time.
Distance covered is same.

Upstream distance = Downstream distance.
(44/5)*v = 4*u
(11/5)*v = u..
11/5 = u/v.

So, from ratio
u = 11.
v = 5.

x = (u + v)/2 and y= (u - v)/2.

x/y = (u + v)/(u - v).
= (11 + 5)/(11 -5 ).
= 16/6.
= 8/3.

Ratio = 8:3.

Let u= man speed & v= stream speed.

We know downstream =u + v & upstream = u - v.

Then,

u - v = 8 + (48/60) = 8.8 hrs for upstream.

u = v = 4hrs for down stream.

Solving we get 6.4/- 2.4 (neglect sign).

Now, 6.4/2.4 = 64/24 = 8/3.

So, the answer is 8:3.

I did not understand anything. Please let me know the easy way for this?

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?