) A water tank is emptying steadily by 2 liters of water per hour. There were 2 liters of water 6 hours after
midnight. Let x represent the number of hours since midnight, and let y represent the number of liters of water
in the tank. Find the equation showing the amount of water at time x
To find the equation showing the amount of water at time x, we need to understand the given information and use it to derive the equation.
According to the problem, the water tank is emptying steadily by 2 liters of water per hour. This means that every hour, the amount of water decreases by 2 liters.
We are also given that there were 2 liters of water in the tank 6 hours after midnight. This means that 6 hours after midnight, the tank had 2 liters of water.
Let's break down the problem and form the equation step by step:
1. At the start, at midnight (x = 0), the amount of water in the tank is unknown. Let's represent it as y0.
2. After 6 hours (x = 6), the amount of water in the tank is given as 2 liters. So, we can say:
y6 = 2
3. Since the tank is emptying steadily by 2 liters per hour, the amount of water in the tank after x hours can be expressed as:
y = y0 - 2x
4. Now, substituting the values we have, we can form the equation:
y6 = y0 - 2(6)
2 = y0 - 12
5. Finally, rearranging the equation to solve for y0:
y0 = 2 + 12
y0 = 14
So, the equation showing the amount of water in the tank at time x is:
y = 14 - 2x