Aptitude - Boats and Streams - Discussion

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.

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.

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.

Let the man's rate upstream be x kmph and that downstream be y kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

i.e.
d=d
44/5 x = 4y
by further solving
11x - 5y =0 i.e. y=11/5x ---> eq(1)

They have x = speed of the boat - speed of the current = u-v.
And y = speed of boat + speed of the current = u + v.

From eq(1).
u-v = 11/5(u + v).
u/v = 8/3.
i.e. u:v = 8:3.

8hr48min we need to convert 8hr48min in terms of only hr because we are required to compare 8hr48min to 4hr....and in 4hr there are no unit of any min therefore we have to convert 8hr48min in only hr ok....and 8 is already given in hr....
so that we will convert only 48min in terms of hr
60min=1hr
1min=1/60
similarly...
60min=1hr
1min=1/60
48min=(1/60)*48=48/60hr

[8(48/60)]hr=8(4/5)=8*5+4=40+4=44

An easy way to solve.

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

Upstream = x-y km/hr.

Downstream = x+y km/hr.

ATQ,

[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).

Speed = Distance/Time.
Downstream = (u-v) km/hr.
Upstream = (u+v) km/hr.

Converting time to mins gives;
8hrs. 48 mins = 528 mins.
4 hrs. = 240 mins.

Let, Distance travelled = x km.

Therefore,
u-v = x/528 ----> 1.
u+v = x/240 ----> 2.

On dividing 1/2.

Therefore, (u-v)/(u+v) = 240/528 = 10/22.
On solving u/v = 32/12 = 8/3.

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.

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).

Boat speed=x,
Water speed=y then.

The upstream speed of boat=(x-y),
And downstream speed of boat=(x+y).

The distance of upstream =speed of downstream
so, distance=speed * time.

(x-y)*528 = (x+y)*240,
(x-y)*(11/5) = (x+y),
11x-11y = 5x+5y,
6x-16y = 0,
6x = 16y,
x/y = 16/6,
x/y = 8/3 (speed of boat/speed of water).