Video: Writing and Solving One-Variable Equations

It took Olivia and Jacob 155 minutes to clean their apartment. Given that Olivia cleaned for 85 minutes longer than Jacob, write an equation to express the amount of time (𝑚) that Olivia spent cleaning. Then solve the equation.

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Video Transcript

It took Olivia and Jacob 155 minutes to clean their apartment. Given that Olivia cleaned for 85 minutes longer than Jacob, write an equation to express the amount of time that Olivia spent cleaning. Then solve the equation.

If we let 𝑚 be the amount of time that Olivia spent cleaning, then Jacob would spend 𝑚 minus 85 minutes cleaning. This is because Olivia cleaned for 85 minutes longer than Jacob. The total amount of time that Olivia and Jacob cleaned for was 155 minutes.

This means that we can write an equation 𝑚 plus 𝑚 minus 85 is equal to 155. Simplifying the left-hand side of the equation gives us two 𝑚 minus 85 equals 155. Adding 85 to both sides of this equation gives us two 𝑚 is equal to 240. And finally, dividing both sides by two gives us a value of 𝑚 of 120.

This means that Olivia cleaned for 120 minutes. As Olivia cleaned for 120 minutes, Jacob must have cleaned for 35 minutes, as 120 minus 85 is equal to 35. These two numbers add up to the total time of 155 minutes.

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