marcus and will are painting a barn. Marcus paints twice as fast as Will. On the first day, they have worked for 6 hours and completed 1/3 of the job when Will gets injured. If Marcus has to complete the rest of the job by himself, how many additional hours will it take him?
18 hours
To solve this problem, we need to determine the relative painting rates of Marcus and Will, and then use that information to calculate the additional time it would take Marcus to finish the job by himself.
Let's start by assigning variables to Marcus and Will's painting rates. Let's say that Marcus paints at a rate of 1 unit per hour, so his rate can be represented by 1 unit/hour. Since Marcus paints twice as fast as Will, we can say that Will's rate is 1/2 unit/hour.
Next, let's calculate how much work Marcus and Will complete together in 6 hours. Marcus paints at a rate of 1 unit/hour, so in 6 hours, he completes 6 * 1 = 6 units of work. Will paints at a rate of 1/2 unit/hour, so in 6 hours, he completes 6 * 1/2 = 3 units of work.
Since together they have completed 1/3 of the job, we can calculate how much work is needed to complete the entire job. The total work can be represented as 3 * (1/3) = 1 unit.
Since Marcus has to complete the rest of the job by himself, he needs to finish the remaining 1 unit of work. Since his painting rate is 1 unit/hour, it will take him an additional 1/1 = 1 hour to complete the rest of the job.
Therefore, it will take Marcus an additional 1 hour to finish the barn painting by himself.