An empty pool is filled with two different pipes in three and a half hours. The first pipe fills the pool 13 times

An empty pool is filled with two different pipes in three and a half hours. The first pipe fills the pool 13 times faster than the second pipe. Two of the same pools began to be filled using these pipes (the first pool using only the first pipe, and the second pool using only the second pipe). In how many minutes will the first pool receive as much water as the second pool still has to fill?

The solution of the problem.

1. Let’s denote by x the capacity of the pool.

2. Let us denote by y the amount of water that will be poured into the first pool at the moment when as much water is poured into the first pool as remains to be poured into the second pool.

3. How much water will be poured into the second pool by this time?

x – y liters.

4. How much water will be poured into both pools by this time?

y + (x – y) = x liters.

5. In how many minutes do both pipes together pour x liters of water?

in 3.5 hours = 210 minutes.

Answer. The first pool will be filled with as much water as the second pool will still have to be poured after 210 minutes.