A concrete mixing tub contains 34 liters of water and 22 liters of sand. Starting at the same time, water is added to the tub at a rate of 5 liters per minute, while sand is also added to the tub at a rate of 7 liters per minute.

Answer 1

To determine the amounts of water and sand in the concrete mixing tub over time, we can set up equations based on the initial amounts and the rates at which they are added.

Initial amounts:

• Water: 34 liters
• Sand: 22 liters

Rates of addition:

• Water: 5 liters per minute
• Sand: 7 liters per minute

Let \( t \) be the time in minutes.

Amounts after \( t \) minutes:

1. Water: \[ \text{Water after } t \text{ minutes} = 34 + 5t \]

2. Sand: \[ \text{Sand after } t \text{ minutes} = 22 + 7t \]

Summary:

In \( t \) minutes:

• The amount of water in the tub will be \( 34 + 5t \) liters.
• The amount of sand in the tub will be \( 22 + 7t \) liters.

You can plug in specific values for \( t \) to find the amounts of water and sand at any given minute. For example:

• At \( t = 0 \) (initial amounts):

  • Water: \( 34 + 5(0) = 34 \) liters
  • Sand: \( 22 + 7(0) = 22 \) liters

• At \( t = 1 \) minute:

  • Water: \( 34 + 5(1) = 39 \) liters
  • Sand: \( 22 + 7(1) = 29 \) liters

• At \( t = 2 \) minutes:

  • Water: \( 34 + 5(2) = 44 \) liters
  • Sand: \( 22 + 7(2) = 36 \) liters

And so on.