Final answer:
To find how long it will take both pipes to fill the pool, their rates, ⅓ and ⅒ pool/hour, are added together to get ⅑ pool/hour. Thus, it will take 6 hours to fill the pool using both pipes.
Step-by-step explanation:
To determine how long it will take to fill the pool using both pipes, we need to find the rate at which the pool is filled when both pipes are working together. Pipe 1 fills the pool in 9 hours, so its rate is ⅓ of the pool per hour (⅓ pool/hour). Pipe 2 fills the pool in 18 hours, so its rate is ⅒ of the pool per hour (⅒ pool/hour). To find the combined rate, we add both rates together:
- ⅓ pool/hour + ⅒ pool/hour = ⅑ pool/hour
The combined rate is ⅑ pool/hour, meaning together, the pipes fill the pool at a rate of one pool per 6 hours. Therefore, it will take 6 hours to fill the pool using both pipes.