Final answer:
To determine the number of minutes, x, required for Mark to empty the dishwasher working alone, we can set up the equation 3/20 = 1/x. By solving this equation, we find that x = 20/3 minutes.
Step-by-step explanation:
To determine the number of minutes, x, required for Mark to empty the dishwasher working alone, we can use the concept of work rate. Let's assume that Shelley's work rate is represented by the variable S and Mark's work rate is represented by the variable M. According to the given information, Shelley can empty the dishwasher in 10 minutes, so her work rate is 1/10. With help from Mark, they can empty the dishwasher in 4 minutes, so their combined work rate is 1/4. To determine Mark's work rate, we subtract Shelley's work rate from the combined work rate: M = 1/4 - 1/10. Simplifying this expression gives us Mark's work rate as 3/20. Since work rate is inversely proportional to time, we can set up the equation M = 1/x, where x represents the number of minutes required for Mark to empty the dishwasher working alone. By substituting the value of Mark's work rate, we get 3/20 = 1/x. Cross-multiplying gives us 3x = 20, and dividing both sides by 3, we find that x = 20/3 minutes. Therefore, it would take Mark approximately 6 and 2/3 minutes to empty the dishwasher working alone.