Aptitude - Boats and Streams - Discussion

Speed downstream = (10 + x) * m/h.
Speed upstream = (10 - x) m/h.
36/(10 - x) - 36/(10 + x) = 90/60.
72** 60 = 90(100 - x ^ 2).
x ^ 2 + 48x - 100 = 0.
(x + 50)(x - 2) = 0.
x = 2m/h.

Since upstream takes 90 minutes more than downstream,
U(time) = 90 mins+ D( time)
Since time = Distance/speed.
D/ S = 90+D/S.
36/(10-x) = 90+36/(10+x).
36/(10-x) - 36/(10+x) = 90/60( converting into hrs)
36(1/10-x-1/10+x) = 3/2,
12((10+x-10+x)/10^2-x^2) = 1/24,
2x(24) = 10^2-x^2,
x^2+48x-10^2 = 0,
x^2+50x-2x-100 = 0,
x(x+50)-2(x+50) = 0,
(x-2)(x+50) = 0,
x=2,-50.
Since we neglect the negative number, then the answer will be 2mph.

Why you have subtracted 36/ (10-x) -36/ (36+x) ? Please explain.

Let's take 2.

Down stream(time taken) - 36/(10+2)= 3hrs.
Up stream (time taken) - 36/(10-2) = 4.5hrs.
Difference = 1.5hrs which is =90min.
So, option A is correct.

36/(10+x) - 36/(10-x) = 90/60.
Take 36common.
36((10+x)-(10-x))/100-x2 = 9/6.
Solve term.

36*2x/100-x2 = 9/x.
Cross multiple the terms,
72x*6 = 900-9x2.
X2+48x-100 = 0.
Take factor,
Get two term x=-50 & x=2.

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).

@Rohit.

Perfect explanation, Thanks.

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.

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.

@Sriteja.

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