Question
A tank at a factory contains water. Workers are draining the tank at a constant rate. After 37 minutes of being drained, the tank contains 546 liters of water. After 58 minutes, the tank contains 294 liters of water.
(a) Choose the statement that best describes how the time and the amount of water in the tank are related. Then fill in the blank.
• As time increases, the amount of water in the tank decreases.
The amount of water in the tank decreases at a rate of liters per minute.
•As time increases, the amount of water in the tank increases.
The amount of water in the tank increases at a rate of I liters per minute.
(b) How much water did the tank contain when the workers started draining it?
• liters
(a) Choose the statement that best describes how the time and the amount of water in the tank are related. Then fill in the blank.
• As time increases, the amount of water in the tank decreases.
The amount of water in the tank decreases at a rate of liters per minute.
•As time increases, the amount of water in the tank increases.
The amount of water in the tank increases at a rate of I liters per minute.
(b) How much water did the tank contain when the workers started draining it?
• liters
Answers
GPT-4o mini
To solve the problem, first, we need to determine the rate at which the tank is being drained.
### (a) Analyze the relationship
From the data:
- After 37 minutes, the tank contains 546 liters.
- After 58 minutes, the tank contains 294 liters.
Now we can calculate the change in the amount of water over the change in time:
1. Find the amount of water drained:
- Amount of water at 37 minutes: 546 liters
- Amount of water at 58 minutes: 294 liters
- Water drained = 546 liters - 294 liters = 252 liters
2. Find the change in time:
- Time at 58 minutes - Time at 37 minutes = 58 - 37 = 21 minutes
3. Calculate the rate of water drained per minute:
- Rate = Water drained / Time = 252 liters / 21 minutes = 12 liters/minute
Now we can fill in the blank with the correct rate:
• As time increases, the amount of water in the tank decreases.
The amount of water in the tank decreases at a rate of **12 liters** per minute.
### (b) Determine the initial amount of water
To find out how much water was initially in the tank when the workers started draining, we can use the information after 37 minutes.
Let \( W \) be the initial amount of water in the tank. Using the rate of drainage:
- Amount of water after 37 minutes: \( W - 12 \times 37 = 546 \)
- Thus, \( W - 444 = 546 \)
- Therefore, \( W = 546 + 444 \)
- \( W = 990 \)
So, when the workers started draining the tank, it contained **990 liters** of water.
### Summary
(a) The amount of water in the tank decreases at a rate of **12 liters** per minute.
(b) The tank contained **990 liters** when the workers started draining it.
### (a) Analyze the relationship
From the data:
- After 37 minutes, the tank contains 546 liters.
- After 58 minutes, the tank contains 294 liters.
Now we can calculate the change in the amount of water over the change in time:
1. Find the amount of water drained:
- Amount of water at 37 minutes: 546 liters
- Amount of water at 58 minutes: 294 liters
- Water drained = 546 liters - 294 liters = 252 liters
2. Find the change in time:
- Time at 58 minutes - Time at 37 minutes = 58 - 37 = 21 minutes
3. Calculate the rate of water drained per minute:
- Rate = Water drained / Time = 252 liters / 21 minutes = 12 liters/minute
Now we can fill in the blank with the correct rate:
• As time increases, the amount of water in the tank decreases.
The amount of water in the tank decreases at a rate of **12 liters** per minute.
### (b) Determine the initial amount of water
To find out how much water was initially in the tank when the workers started draining, we can use the information after 37 minutes.
Let \( W \) be the initial amount of water in the tank. Using the rate of drainage:
- Amount of water after 37 minutes: \( W - 12 \times 37 = 546 \)
- Thus, \( W - 444 = 546 \)
- Therefore, \( W = 546 + 444 \)
- \( W = 990 \)
So, when the workers started draining the tank, it contained **990 liters** of water.
### Summary
(a) The amount of water in the tank decreases at a rate of **12 liters** per minute.
(b) The tank contained **990 liters** when the workers started draining it.