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 10 mph, the speed of the stream is:

12 mph
22.5 mph
33 mph
44 mph

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let the speed of the stream x m p h . Then, \\ Speed downstream = (10 + x) m p h, \\ Speed upstream = (10 - x) m p h . \\ ∴ \frac{36}{(10 - x)} - \frac{36}{(10 + x)} = \frac{90}{60} \\ \Rightarrow 72 x \times 60 = 90 (100 - x^{2}) \\ \Rightarrow x^{2} + 48 x - 100 = 0 \\ \Rightarrow (x + 50) (x - 2) = 0 \\ \Rightarrow x = 2 m p h \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{stream}}\,x\,mph.\,{\text{Then}}, \cr & {\text{Speed}}\,{\text{downstream}} = \left( {10 + x} \right)\,mph, \cr & {\text{Speed}}\,{\text{upstream}} = \left( {10 - x} \right)\,mph. \cr & \therefore \frac{{36}}{{\left( {10 - x} \right)}} - \frac{{36}}{{\left( {10 + x} \right)}} = \frac{{90}}{{60}} \cr & \Rightarrow 72x \times 60 = 90\left( {100 - {x^2}} \right) \cr & \Rightarrow {x^2} + 48x - 100 = 0 \cr & \Rightarrow \left( {x + 50} \right)\left( {x - 2} \right) = 0 \cr & \Rightarrow x = 2\,mph \cr}$