Final answer:
Together, Jane and Alice can clean the house in 1 hour and 52.5 minutes since their combined rate of cleaning is 8/15 of the house per hour.
Step-by-step explanation:
Jane and Alice are working together to clean a house and we need to determine how long it will take them. To calculate their combined rate of work, we can add their individual rates. Jane cleans the house in 3 hours, so her rate is 1/3 of the house per hour. Alice cleans the house in 5 hours, which means her rate is 1/5 of the house per hour. Working together, their combined rate is 1/3 + 1/5 = 5/15 + 3/15 = 8/15 of the house per hour. To find out how long it takes to clean the whole house together, we calculate the reciprocal of their combined rate: 15/8 hours, which is 1 hour and 52.5 minutes.