Braininvat » Wed Dec 20, 2017 11:15 am wrote:Just express the surface area of the shed in units that are a multiple of 3 and 5. Say 30 square meters. One painter has a paint rate of 10 m/hr, the other of 6 m/hr. So their combined rate is 16 m/hr. Easy peasy. 1 and 7/8 hours.
Very clever
Braininvat. I can't remember at all where I saw the question, but it has been cropping up in my mind the last week.
My first tendency was to say that if one did it in 3 and the other in 5, then the average time would 4. So together they would do it in 2 h. But something did not seem right about that. The problem has cropped up in my daydreaming a few times, and then last night, during a twilight sleep, I rationalised that one could paint 5/8ths of the area in the same time as the other did 3/8ths. Number one could paint the whole area of the shed in 180 mins, which meant he could paint 5/8ths of it in 112.5 minutes. As a check, it meant that the other could paint his share in 3/8ths of 300 minutes, which is 112.5 minutes or 1 and 7/8 h.
Area was also not relevant in the way I worked it out, but Lomax was more probably more systematic than intuitive in applying algebra.
Anyhow thank you all for playing.