Video: Ratio in a Real-World Context

The table shows the relation between time (in hours) and the distance a car traveled (in kilometers). Find the values of π‘Ž, 𝑏, and 𝑐.

02:41

Video Transcript

The table shows the relation between time in hours and the distance a car travelled in kilometers. Find the value of π‘Ž, 𝑏, and 𝑐.

Here, our π‘Ž, 𝑏, and 𝑐 in a chart. So the time row is in hours and the distance row is in kilometers. So the only relationship where we know the time and distance is here: in 15 hours, the car travelled 1425 kilometers. So again, the car travelled 1425 kilometers in 15 hours. So to really know how they’re related, let’s find out how far the car travels in one hour. This way we can fill out the rest of the chart.

So we can divide both numbers by 15, creating the relationship that the car travels 95 kilometers per hour. So in order to find π‘Ž, that’s a time, so we want to take the distance and divide by the 95 kilometers that will tell us how many hours it took. And 1615 divided by 95 is 17. So it will take the car 17 hours to travel that distance.

𝑏 and 𝑐 are distances. So to find 𝑏, it says that there’s a time of 13 hours. So if we travel 95 kilometers in one hour, we need to take the13 hours and multiply it by 95. And 13 times 95 is equal to 1235 and this would be in kilometers. So 𝑏 is equal to 1235.

And now, lastly, for 𝑐, we find it in the same way we found 𝑏 because we’re given 20 which is a time, so 20 hours we need to multiply by 95. And 20 times 95 is equal to 1900 and this is in kilometers. So 𝑐 is equal to 1900. So π‘Ž is equal to 17, 𝑏 is equal to 1235, and 𝑐 is equal to 1900.

And since our relationship was one hour equals 95 kilometers, a way that we could check our work would be to take each of the times and multiply it by 95 since that was our relationship. And after doing so, we would still get our final answer of π‘Ž equals 17, 𝑏 is equal to 1235, and 𝑐 is equal to 1900.

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