## Task 6 - 320736

The following information was given about a swimming pool:

The pool can be filled through two separate water pipes. From the second pipe, 50 cubic meters more flow out per minute than from the first. To completely fill the pool, 48 minutes are required if both pipes are opened simultaneously; in contrast, 2 hours are needed if only the first pipe is opened.

Determine whether the volume of the pool can be uniquely determined by these statements! If this is the case, determine this volume!
If the volume of the tank is $x$ cubic meters, it follows from the given information: In each minute, $\frac{x}{120}$ cubic meters flow from the first open pipe, and $\left(\frac{x}{120}+50\right)$ cubic meters from the second pipe. The volume of the tank that is filled by both pipes in 48 minutes is therefore

$$
48 \cdot\left(\frac{x}{120}+\left(\frac{x}{120}+50\right)\right)
$$

cubic meters. Thus, the equation

$$
48 \cdot\left(\frac{x}{120}+\left(\frac{x}{120}+50\right)\right)=x
$$

must hold. By rearranging, we get $x=12000$.

Therefore, it is uniquely determined by the given information: The volume of the tank is 12000 cubic meters.

Solutions of the 3rd round 1992 adopted from [5]

# 4.35 XXXIII. Olympiad 1993 

### 4.35.1 1st Round 1993, Class 7