Video: Solving Proportion Equations Involving Direct Variation in a Real-World Context

A car moves a uniform velocity where distance varies directly with time. If the car travels a distance of 231 km in 9 hours, how far will it travel in 15 hours?

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Video Transcript

A car moves a uniform velocity where distance varies directly with time. If the car travels a distance of 231 kilometers in nine hours, how far will it travel in 15 hours?

It’s very important to know that the distance varies directly with time. Because now we can write an equation based on how the distance and the time are related. 𝑑 equals 𝑘𝑡. 𝑑 is equal to distance and 𝑡 is equal to time. 𝑘 is a variable that lets us know that they vary directly with each other. We know that the distance is 231 kilometers. And the car travelled that distance in nine hours. So we can solve for 𝑘 by dividing both sides of the equation by nine hours.

231 divided by nine give us the value of the variable 𝑘 to be around 25.67 kilometers per hour. So now we can create an equation to answer our question: how far will it travel in 15 hours. So we can plug in for 𝑘. So 𝑑 equals 25.67 kilometers per hour times 𝑡. So we’re wanting to know how far it will travel, so we’re solving for 𝑑, in 15 hours. So we need to plug in 15 hours for 𝑡. So first, we can see the hour variables cancel. So we’re left with kilometers, which makes sense because we should be getting a distance.

So we need to take 25.67 times 15. And we find that the car, after 15 hours, will have travelled 385.05 kilometers.

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