A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance up stream. If the speed of the boat in still water 10 mph, the speed of the stream is

Speed of boat in still water$\text{=10mph}$

Let speed of stream$=x\text{mph}$

Upstream speed$=\left(10-x\right)\text{mph}$

Downstream speed$=\left(10+x\right)\text{mph}$

According to problem

Upstream time$-$ downstream time$=$ 90 minutes

$\frac{36}{10-x}-\frac{36}{10+x}=\frac{90}{60}hrs=\frac{9}{6}$

$\frac{\left(10+x\right)-\left(10-x\right)}{{10}^2-x^2}=\frac{9}{6}\times \frac{1}{36}$

$\frac{10+x-10+x}{100-x^2}=\frac{1}{24}$

$\frac{2x}{100-x^2}=\frac{1}{24}$

$48x=100-x^2$

$x^2+48x-100=0$

$x^2-2x+50x-100=0$

$x\left(x-2\right)+50\left(x-2\right)=0$

$\left(x-2\right)\left(x+50\right)=0$

$x=2\left(\text{or}\right)x=-50$

Speed is always positive

$\therefore$ $x=2\text{mph}$