A boat takes 90 Minutes less to travel 36 Miles downstream than to travel the same distance upstream.If the speed of the boat in still water is 10mph , the speed of the stream is :
I have tried:
let distance be 36 ,td be time taken for downstream and tu be time taken for upstream
speed = distance/time
36/td - 36/tu = 90
36(1/td - 1/tu)= 90
can you guide me for the answer I dont have an idea about doing the sum
The speed of the stream is $x$, then $10+x, 10-x $ are the speeds of the boat going down and upstream respectively. Then the down and upstream times are $\dfrac{36}{10+x}, \dfrac{36}{10-x}$. So: $\dfrac{36}{10+x} + 1.5 = \dfrac{36}{10-x}$. Can you proceed to find $x$?
Remember that - Speed of boat in downstream = speed of boat in still water + Stream speed.
Similarly,
Speed of boat in upstream = Speed of boat in still water - Stream speed.
Let Stream speed = x
Downstream speed = 10 + x
Upstream speed = 10 - x
Then,
$\frac{36}{10 - x} - \frac{36}{10 + x} = \frac{90}{60}$
$36\left(\frac{10 + x - 10 + x}{(10 - x)(10 + x)}\right) = \frac{3}{2}$
$12\left(\frac{2x}{(100 - x^2)}\right) = \frac{1}{2}$
Cross multiply terms,
$48x = 100 - x^2$
$x^2 + 48x - 100 = 0$
$x^2 + 50x - 2x - 100 = 0$
$x(x + 50) - 2(x + 50) = 0$
$(x - 2)(x + 50) = 0$
x = 2, -50
Speed can't be negative in this case. So x = 2 is answer.