Writing equations for relationships between quantities | 6th grade | Khan Academy

TL;DR

Learn how to write equations to calculate the time it takes to walk a certain distance at a constant rate, and how to use proportions to find the amount of water based on the amount of vegetable stock.

Transcript

• [Narrator] We're told Amad is going to walk 20 kilometers for a charity fundraiser. In the first part of this question, they say, write an equation that represents how many hours, t, the walk will take if Amad walks at a constant rate of r kilometers per hour. Pause this video and see if you could have a go at that. All right, now let's work thro... Read More

Key Insights

• ☠️ The equation for calculating time based on distance and rate is t = 20/r.
• 💦 The equation for finding the amount of water based on vegetable stock is w = (4/5)v.
• 🔨 Proportions are a useful tool for solving problems involving relationships between different quantities.
• ☠️ The rate in the equations represents the independent variable, while the time and amount of water represent the dependent variables.
• 🚶 Equations can be used to solve for unknown variables in various scenarios, such as walking distances and cooking recipes.
• 👻 Understanding how to manipulate equations allows for quick calculations and problem-solving.
• 🍳 Proportions can be used in real-life situations, such as determining ingredient quantities for cooking.

Questions & Answers

Q: How can we write an equation to calculate the time for a walk at a constant rate?

The equation is t = 20/r, where t is the time in hours and r is the rate in kilometers per hour. This equation allows us to find the time based on the given rate of walking.

Q: If Amad walks at a constant rate of 6 kilometers per hour, how many hours will the walk take?

By substituting the rate of 6 into the equation, we get t = 20/6, which simplifies to 3 and 1/3 hours or 3 hours and 20 minutes.

Q: How can we find the amount of water to use based on the amount of vegetable stock?

We can use the proportion equation w = (4/5)v, where w is the amount of water in milliliters and v is the amount of vegetable stock in milliliters. This equation allows us to calculate the water needed for any given amount of vegetable stock.

Q: If there are 800 milliliters of unused vegetable stock, how much water should the restaurant use to make soup?

By substituting the value of 800 into the equation, we get w = (4/5)800, which simplifies to 640 milliliters. The restaurant should use 640 milliliters of water to make soup.

Summary & Key Takeaways

• The first part explains how to write an equation to calculate the time it takes to walk a distance at a constant rate. The equation is t = 20/r, where t is the time in hours and r is the rate in kilometers per hour.

• The second part demonstrates how to use proportions to find the amount of water to use based on the amount of vegetable stock. The equation is w = (4/5)v, where w is the amount of water in milliliters and v is the amount of vegetable stock in milliliters.