# Question 89c39

Sep 26, 2017

$20$ and $5$.

#### Explanation:

Let the speed of the boat be $x$ $\text{miles/hour}$ and the speed of the current be $y$ $\text{miles/hour}$.

In down stream the trip $\left(x + y\right)$ $\text{miles}$ takes in $1$ hour. so, $825$ $\text{miles}$ takes $\frac{825}{x + y}$ $\text{hours}$.

Hence, as per question

$\frac{825}{x + y} = 33 \text{ "" } \left(i\right)$

Again, in the trip back, $\left(x - y\right)$ $\text{miles}$ take $1$ hour. Hence $825$ $\text{miles}$ take $\frac{825}{x - y}$ $\text{hours}$.

Hence, as per question

$\frac{825}{x - y} = 55 \text{ "" } \left(i i\right)$

From equation $\left(i\right)$, we get

$\frac{825}{x + y} = 33$

or

$x + y = \frac{825}{33} = 25 \text{ "" } \left(i i i\right)$

From equation (ii#), we get

$\frac{825}{x - y} = 55$

or

$x - y = \frac{825}{55} = 15 \text{ "" } \left(i v\right)$

Now, solving equations $\left(i i i\right)$ and $\left(i v\right)$, we get

$x = 20 \mathmr{and} y = 5$

Hence, the speed of the boat is $\text{20 miles/hours}$ and the speed of the current is $\text{5 miles/hours}$.