Final answer:
The slower landscaper would take 22.5 hours to complete the job alone, while the faster one would take 15 hours. This is calculated by using the combined work rate of two landscapers who work together to complete the job in 9 hours and knowing that one works 1.5 times as fast as the other.
Step-by-step explanation:
The question involves determining the individual times two landscapers would take to complete a certain job when they work together and one of them works 1.5 times as fast as the other, and it takes 9 hours for them to complete the job when working together. To solve this, we will use the concept of work rates.
Let x be the amount of time it takes the slower landscaper to complete the job alone.
Then, the faster landscaper who works 1.5 times as fast will take x/1.5 hours to complete the job alone.
The amount of work done is the inverse of the time taken. Therefore:
- Slower landscaper's work rate is 1/x jobs per hour.
- Faster landscaper's work rate is 1.5/x jobs per hour.
Their combined work rate when working together is:
(1/x) + (1.5/x) = 1/9 (since they finish the job in 9 hours together)
Solving for x, we combine the work rates:
2.5/x = 1/9
Now, multiplying both sides by 9x to clear the fractions yields:
2.5 * 9 = x
22.5 = x
Therefore, the slower landscaper takes 22.5 hours to complete the job alone, and the faster one takes 22.5/1.5, which is 15 hours to complete the job alone.