Aptitude - Boats and Streams - Discussion

By using the formula we have;
Speed upstream = u-v.
Speed downstream= u+v.
Where u&v is speed of the boat in still water and speed of stream respectively.
Given that distance covered is equal so;

By the time distance formula;
Speed *time= distance.
Both the values put according to formula.
(u-v) *8*48/60=(u+v) 4.
(u-v) 8*4/5=(u+v) 4.
44/5u-44/5v= 4u+4v.
44/5u- 4u = 44/5v+4v.
u[44/5-4] = v[44/5+4].
24u = 64v.
u/v = 64/24.
u/v = 8/3.

So, the ratio between the speed of the boat and speed of the water current is;
8:3.

Let,

Upstream speed = X kmph.
Downstream spead = Y kmph.

So,
We know that distance is the same.
And we know, D=SXT (speedxtime)
D= X(8+48/60) upstream case--->eq1
D=Y(4)---> eq 2
Now, equate both.

4Y = X(8+4/5).
4Y= X(44/5).
Y=X(11/5).
Y/X = 11/5.

So now relate as Y=11, X=5.
Now speed of water(S.W) = downstrean-upstream/2.
= Y-X/2.
=11-5/2 = 6/2 = 3.

Now, speed of boat = downstream - speed of the water.
= Y- (S.W).
= 11-3 = 8.

Now ratio of both as given in question,
Ratio of boat speed to water speed = 8/3.
Ratio = 8:3.
Hope you'll get it well.

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?

Thank you everyone for explaining.

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.

When the same distance is mentioned in this type of question best shortcut is the sum:difference. Nothing but 12hr 48 min: 4hr 48min.

Other than change completely minutes. so 768min:288 min = 8:3

@All.

You did not mention which speed of the boat to be calculated if it was in the still water or downstream or against the stream!

Thanks for this short trick @Mahesh.

Distance Upstream = Distance Downstream.

Speed Upstream * Time Upstream = Speed Downstream * Time Downstream.
(x - y) * 44/5 = (x + y) * 4,
24x = 64y,
x:y = 8:3.

Given,
Time (upstream)=8 hour 48 min=(8*60+48) = 528 min.
Time (downstream)= 4 hour = (4*60)min = 240 min.

Let distance be x.
we know speed =distance/time.
so, the speed of the boat (upstream) = distance/time.
= x/528.
speed of the boat (downstream) = distance/time.
= x/240.

We know that;
speed of boat in still water = (downstream+upstream)/2.
= (x/240 + x/528)/2.
= x/330.

We know that
speed of stream/current water.
= (downstream-upstream)/2.
So we have to find the ratio of the speed of the boat in still water by the speed of the stream/current =
(x/330)/(x/528)=8/3 or 8:3
Therefore, ratio = 8:3 Answer.