Kinesys pops into a residential neighborhood on Abakos, where every house has an abacus hanging by the door instead of a doorbell. “Abakos,” Liz sighs, reading the map. “We set a completely different course.”
In front of a little house, three Abakian painters are bickering, furiously sliding the beads of an abacus: each one swears he’s the fastest. The exasperated homeowner doesn’t care who’s right. He just wants to know how long the job will take if all three get to work together. On Abakos, after all, a wrong estimate is an unforgivable breach of manners.
“Finally, a serious problem,” says Dord, visibly relieved. M00N floats beside him: “See? You’re going to love this planet!”
The Riddle
The first painter paints a room in one hour, the second paints the same room in an hour and a half, and the third paints the same room in two hours. If they all paint the same room together, how long will it take them?
Hint
Instead of thinking about times, think about how much work each one does. Pick a convenient stretch of time in which each of the three, working alone, would paint a whole number of rooms.
Solution
Consider a stretch of 6 hours, that is, 360 minutes: a handy number, because it makes every calculation come out in whole numbers. In 6 hours:
- the first painter, alone, would paint 6 rooms;
- the second, alone, would paint 4 rooms;
- the third, alone, would paint 3 rooms.
Working together for 6 hours, they would paint 6 + 4 + 3 = 13 rooms. To find how long one room takes, just divide the 6 hours by 13:
6 hours / 13 = 360 min / 13 = 27 minutes, 41 seconds, and 54 hundredths (approximately).
The homeowner recorded the result on his abacus, down to the hundredth. Dord approved.