Aptitude - Boats and Streams - Discussion

D/S = T.
Time difference is 90.
We have to convert miles per HOUR.
So (36/10-x)-(36/10+x) = 90/60.

Let the speed of the stream be x mph.

Then sp. Downstream=(10+x) mph.

Sp. Upstream =(10-x) mph.
(36/10-x) - (36/10-x) =90/60.

Can be written as (36/10-x)- (36/10-x) = 9/6,

[360+36x-360+36x]6 = 9(10^2-x^2),

72x * 6= 900-9x^2,
9x^2+432x-900=0,
x^2 +48x -100=0.
(x+50)(x-2),
X=2mph.

Let upstream time be T hrs.
Then, downstream time will be T-3/2 hrs.
Upstream - downstream = T - T + 3/2 = 3/2 hrs = 90 minutes.

I am not getting this, please explain me.

Upstream ditsnace = downstream distance.
90/60*(10-x) = (10+s),
300 = 150*x,
X = 2.

@Sriteja.

There is "less" is given in the qn that's why we subtracting the upstream and downstream.

We have a formula,

The speed of boat = (Upstream speed + downstream speed)/2 -----> (1)
Let the actual time be x, then upstream speed = Distance/time =>36/(x-3/2),
<--3/2 came from coverting 90 min to hrs.-->
Similarly, downstream speed will be = 36/x.
Therefore, according to the Formula above (1), ( 36/(x-3/2) +36/x ) /2 = 10.
Onsolving we get Quadratic eqn as: 10x2- 51x +27 = 0.
I don't understand how this :x2 + 48x - 100 = 0 came?

Please help me to solve it.

72x / 100 - x^2 = 90/60.
72x * 60 = 90 *(100-x^2),
72x * 60 = 9000 - 90x^2,

Dividing throughout by 90.
(72x * 60) / 90 = 9000/90 - 90x^2.
48x = 100 - x^2.
x^2 + 48x - 100 = 0.
x^2 +50x - 2x -100 = 0.
x(x + 50) -2(x + 50) = 0.
(x + 50) (x-2) = 0.

@Rohit.

Perfect explanation, Thanks.

Convert 90 minutes into hours, therefore 90/60 = 3/2 hours,
Given that, the speed of the boat in still water = 10,
Let, speed of the stream = x,
Then,
Downstream = 10+x,
Upstream = 10-x.

According to the condition,
3/2 (10-x) = (10+x),
So, 15-1.5x = 10+x,
So, 2.5x = 5,
So, x = 2 (ans).