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To paint the room working alone, we need to find the individual painting rates of each person.
Let's say:
- John's painting rate is J rooms per hour
- Rick's painting rate is R rooms per hour
- Molly's painting rate is M rooms per hour
From the given information, we have the following equations:
1/J + 1/R + 1/M = 1/5 (work done in 5 hours working together)
1/M = 1/14 (Molly can paint the room in 14 hours)
1/R = 1/3 (Rick can paint the room in 3 hours)
1/J = 1/10 (John can paint the room in 10 hours)
Now we can substitute the values of 1/M, 1/R, and 1/J into the first equation:
1/10 + 1/3 + 1/14 = 1/5
(42 + 140 + 30) / 420 = 1/5
212 / 420 = 1/5
0.505 = 0.2
Thus, John can paint the room alone in 10 hours, Rick in 3 hours, and Molly in 14 hours.