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:
2 mph
2.5 mph
3 mph
4 mph
Explanation:
Let the speed of the stream $ x $ mph. Then,
Speed downstream = 10 + $ x $ mph,
Speed upstream = 10 - $ x $ mph.
| $\therefore \dfrac{36}{(10 - x)} $-$ \dfrac{36}{(10 + x)} $=$ \dfrac{90}{60} $ |
$\Rightarrow$ 72$ x $ x 60 = $90 \left(100 - x^2\right)$
$\Rightarrow$ $ x $2 + 48$ x $ - 100 = 0
$\Rightarrow$ $ x + 50\left( x - 2\right)$ = 0
$\Rightarrow$ $ x $ = 2 mph.