Final answer:
To find out how long it would take for Michael's father to finish the puzzle on his own, we can use the concept of work rates. By setting up an equation involving their work rates, we can determine the time it would take for his father to complete the puzzle on his own. The answer is approximately 3 minutes.
Step-by-step explanation:
To find out how long it would take for Michael's father to finish the puzzle on his own, we can use the concept of work rates. Let's assume that Michael completes 1 puzzle in 28 minutes, and his father completes 1 puzzle in x minutes. Therefore, Michael's work rate is 1 puzzle per 28 minutes, and his father's work rate is 1 puzzle per x minutes.
When they work together, the total work rate is the sum of their individual work rates. So, the equation becomes: 1/28 + 1/x = 1/17.
To solve this equation, we can multiply both sides by 28x to get rid of the fractions and simplify the equation. This will give us 17x + 28 = 28x. Then, we can subtract 17x from both sides to get 28 = 11x. Finally, we can divide both sides by 11 to find the value of x, which is the time it would take for Michael's father to finish the puzzle on his own.
Therefore, the answer is x = 28/11 = 2.54. Rounded to the nearest minute, it would take his father approximately 3 minutes to finish the puzzle on his own.