Problem 233: Parting painters
You may need to brush up on your math to solve this problem submitted by Jim Kleyn of Santee, Calif.
Skippy Switzle and B.J. McNichol recently devoted their spring break to painting neighborhood garages. Their original business plan was to earn enough money for new ten-speed bikes. Neighboring folks were happy for the help, and the duo quickly whitewashed its way well into the black. A cigar box full of crumpled green bills had B.J. carrying on about water bottles and rearview mirrors for their dream bikes. That is until half way through old Mr. Winker's garage when Skippy noticed he was doing more than his fair share of the work. While rolling the ceiling, Skippy figured that the duo can paint a garage in 3 hours working together. He also deducted that when he paints a garage by himself it takes him five hours.
Skippy confronted B.J., who was nursing a root beer, but his partner adamantly defended his workmanship. After all, B.J. said, his slow rolling technique results in a higher-quality paint job than Skippy's and his extended soda pop breaks help him maintain focus on the job.
Fed up with excuses, Skippy gave B.J. an ultimatum – 60/40 profit sharing, or no painterly partnership. Not one to compromise, B.J. promptly replied with a knuckle sandwich. Punches and paint cans flew, and the business was dissolved. B.J. decided he didn't need Skippy to make a buck and started up his own painting enterprise. Without changing his work habits, how long will it take B.J. to paint a garage on his own?
