Video Transcript
The level of water in tank A is twice the level of water in tank B. Joseph made a hole in tank A such that the level of water dropped by two inches every second. And at the same time, Danny poured water in tank B such that the level of water in it increased by three inches every second. If it took four seconds for the level of water to be the same in the two tanks, what was the initial level of water in tank B?
If we let the initial level of water in tank B equal 𝑥 inches, then as tank A is twice the level of water as tank B, its initial level will be two 𝑥 inches. We also know that tank A loses two inches per second, whereas tank B gains three inches per second. We’re also told that, after four seconds, the level of water in tank A is equal to the level of water in tank B.
Tank A started with a level of two 𝑥. It drops two inches every second. Therefore, after four seconds, it will have dropped eight inches, as two multiplied by four is equal to eight. Tank B started with a water level of 𝑥 inches. As it gains three inches per second, after four seconds, it will have gained 12 inches. Three multiplied by four is equal to 12.
We therefore have the equation that two 𝑥 minus eight is equal to 𝑥 plus 12. Adding eight to both sides of this equation gives us two 𝑥 is equal to 𝑥 plus 20, as 12 plus eight equals 20. Subtracting 𝑥 from both sides of this new equation gives us 𝑥 is equal to 20, as two 𝑥 minus 𝑥 is equal to 𝑥.
We can therefore say that the initial level in tank B is 20 inches. If the initial level in tank B was 20 inches, then the initial level in tank A must have been 40 inches, as 20 multiplied by two is equal to 40. After four seconds, both tanks will have a water level of 32 inches. Tank B has lost eight inches. 40 minus eight is equal to 32. And tank B has gained 12 inches. 20 plus 12 also equals 32.
