Thanksgiving is coming. Quadmates Judith, Penelope, Ruth, and Virginia are all driving home. Each student has her own car. Willard has come to their dorm room to say goodbye.
Willard asks, “How long do you each have to drive to get home?”
The women reply as follows:
We each have a different whole number of hours to drive.
The sum of these four numbers is less than eighteen.
The product of these numbers is our dorm room number.
Judith has the shortest drive, followed by Penelope, Ruth and Virginia, in that order.
Willard thinks for a little while, and scribbles some notes on a pad, but can not determine the four numbers.
He asks whether any one of the women has to drive just one hour to get home.
The women answer him, and he immediately knows the four numbers.
1. How long does each woman have to drive to get home?
2. What is the women’s dorm room number?
Solutions must include an explanation.