# Video: Writing an Inequality to Represent a Constraint or Condition in a Real-World Problem

Matthew ran 600 meters in 90 seconds, while Sophia was at least 9 seconds ahead of him. Write an inequality to represent the time Sophia finished the 600 meter run.

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### Video Transcript

Matthew ran 600 meters in 90 seconds, while Sophia was at least nine seconds ahead of him. Write an inequality to represent the time Sophia finished the 600-meter run.

So we are writing an inequality, which is less than, greater than, less than or equal to, greater than or equal to, meaning not an equation, not an equal sign, to represent time. So the fact that the race was 600 meters long doesn’t matter. We’re talking about the time, the 90 seconds.

So Matthew ran it in 90 seconds. And Sophia was at least nine seconds faster than that. So if we are faster than someone, we ran the race faster, in a shorter amount of time. So she must have ran it less than 90 seconds because she was faster.

So Sophia’s time is less than Matthew’s time. We know that much. And Matthew’s time was 90 seconds. So we know that Sophia ran it in less than 90 seconds. And we know that Sophia was at least — so instead of less than, let’s change it to “at least,” so less than or equal to — nine seconds faster than Matthew. So let’s take off nine seconds from his time.

So we have Sophia is less than or equal to 90 minus nine. So we can let Sophia’s time be represented by 𝑥. And then 90 minus nine would be 81. So if Sophia was at least nine seconds faster than Matthew, then she ran it in less than or equal to 81 seconds. So the inequality to represent the time Sophia finished the 600-meter run is 𝑥 is less than or equal to 81.