container a has 200 l of water, and is being filled at a rate of 6 liters per minute. container b has 500 l…
container a has 200 l of water, and is being filled at a rate of 6 liters per minute. container b has 500 l of water, and is being drained at 6 liters per minute. how many minutes, m, will it take for the two containers to have the same amount of water?
Answer
Explanation:
Step1: Set up equations for water amounts
Let (m) be the number of minutes. The amount of water in container A after (m) minutes is (200 + 6m). The amount of water in container B after (m) minutes is (500-6m).
Step2: Set the two - equations equal
We want to find when the two containers have the same amount of water, so we set (200 + 6m=500 - 6m).
Step3: Solve for (m)
Add (6m) to both sides: (200+6m + 6m=500-6m+6m), which simplifies to (200 + 12m=500). Then subtract 200 from both sides: (12m=500 - 200=300). Divide both sides by 12: (m=\frac{300}{12}=25).
Answer:
25