A man who can swim 48meter/minute in still water swims 200meter against the current and 200 meters with the current. If the difference between these two times is 10 minutes, then what is the speed of the current?

The correct answer is 32 (which represents 32 meters/minute).

Let us denote the speed of the current as $c$ meters/minute.
The speed of the man in still water is given as $48$ meters/minute.

When the man swims with the current (downstream), his effective speed is the sum of his speed in still water and the speed of the current:
$v_{\text{downstream}}=48+c$ meters/minute.

When the man swims against the current (upstream), his effective speed is the difference between his speed in still water and the speed of the current:
$v_{\text{upstream}}=48-c$ meters/minute.

The time taken to swim a distance of 200 meters against the current is:
$t_{\text{against}}=\frac{200}{48-c}$ minutes.

The time taken to swim a distance of 200 meters with the current is:
$t_{\text{with}}=\frac{200}{48+c}$ minutes.

We are given that the difference between these two times is 10 minutes. Since swimming against the current is slower, $t_{\text{against}}$ is larger than $t_{\text{with}}$. Therefore, we can write the equation:
$\frac{200}{48-c}-\frac{200}{48+c}=10$

We can simplify this equation by dividing both sides by 10:
$\frac{20}{48-c}-\frac{20}{48+c}=1$

Now, let us combine the fractions on the left-hand side over a common denominator:
$20·\left(\frac{(48+c)-(48-c)}{(48-c)(48+c)}\right)=1$

Simplify the numerator inside the parentheses:
$48+c-48+c=2c$

Substitute this back into the equation:
$20·\frac{2c}{{48}^2-c^2}=1$

Multiply both sides by ${48}^2-c^2$:
$40c=2304-c^2$

Rearrange this into a standard quadratic equation form:
$c^2+40c-2304=0$

To solve for $c$, we can factor the quadratic equation. We look for two numbers that multiply to $-2304$ and add up to $40$.
These two numbers are $72$ and $-32$ since:
$72·(-32)=-2304$ and $72+(-32)=40$.

Thus, we can write the factored equation as:
$(c+72)(c-32)=0$

This gives two possible solutions for $c$:
$c=-72$ or $c=32$.

Since the speed of the current must be positive, we discard the negative solution.
Therefore, the speed of the current is $32$ meters/minute.