Math Problem Statement

A water tank initially contained 53 liters of water. It is being drained at a constant rate of 2.5 liters per minute.

How many liters of water are in the tank after 104 seconds? Round answers to the nearest whole liter.

Solution

To determine how many liters of water remain in the tank after 104 seconds, we first need to convert the time into minutes, because the rate at which the water is being drained is given in liters per minute.

Step 1: Convert seconds to minutes

104 seconds=10460 minutes1.7333 minutes104 \text{ seconds} = \frac{104}{60} \text{ minutes} \approx 1.7333 \text{ minutes}

Step 2: Calculate how much water has been drained

The rate of drainage is 2.5 liters per minute, so we calculate the amount of water drained in 1.7333 minutes: Water drained=2.5×1.73334.3333 liters\text{Water drained} = 2.5 \times 1.7333 \approx 4.3333 \text{ liters}

Step 3: Subtract the drained water from the initial amount

Initially, the tank contained 53 liters of water. The remaining water after 104 seconds is: Remaining water=534.333348.6667 liters\text{Remaining water} = 53 - 4.3333 \approx 48.6667 \text{ liters}

Step 4: Round to the nearest whole liter

The remaining water is approximately 49 liters.

Thus, after 104 seconds, 49 liters of water remain in the tank.

Would you like more details or have any questions?

Here are some related questions you might find useful:

  1. How long will it take for the tank to be completely empty?
  2. What is the total time required to drain half of the tank?
  3. How much water is left after 2 minutes?
  4. If the rate of drainage changes to 3 liters per minute, how much water will be left after 104 seconds?
  5. What would happen if the tank started with 100 liters of water?

Tip: When working with time units, always make sure to convert them appropriately to match the rate given in the problem.

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Math Problem Analysis

Mathematical Concepts

Unit Conversion
Linear Equations
Basic Arithmetic

Formulas

Water drained = rate × time
Remaining water = initial amount - drained water

Theorems

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Suitable Grade Level

Grades 6-8