Problem:
Doug can paint a room in 5 hours. Dave can paint the same room in 7 hours. Doug and Dave paint the room together and take a one-hour break for lunch. Let be the total time, in hours, required for them to complete the job working together, including lunch. Which of the following equations is satisfied by
Answer Choices:
A.
B.
C.
D.
E.
Solution:
In one hour Doug can paint of the room, and Dave can paint of the room. Working together, they can paint of the room in one hour. It takes them hours to do the job, but because they take an hour for lunch, they work for only hours. The fraction of the room that they paint in this time is
which must be equal to 1 . It may be checked that the solution, , does not satisfy the equation in any of the other answer choices.
The problems on this page are the property of the MAA's American Mathematics Competitions