Three lights make a line
- My son will soon be three years old!
- That is great! How will you celebrate it?
- I thought of putting three lights on a cake.
- It is not original, but it is a good idea.
- The lights will be placed one behind the other in a straight line.
- OK. Any reason why on a line?
- The middle light will be equally far away from the two other lights.
- Will it be a chocolate cake?
- The middle light is twice as high as the two other lights, but thinner. It can burn 4 hours.
- That should be enough. I mean, if your son really needs to take his time to blow it out.
- The other two can burn 4.5 and 9 hours.
- You are not going a bit over board with these lights?
- After a while the top of the three lights will make a straight line. Slanted, yes, but straight.
- When will that happen?
- I thought the one who could find out would get an extra piece of the cake.
- !!!
- What do you think?
- Is ‘You’re crazy!’ an option?
October 31st, 2008 at 12:24 am
If the tops make a straight line, then the middle candle must have a height that is the average of the outer two at time t. Assuming the outer candles have a height of 1 (so the inner has height 2), then
2(4-t)/4 = [(4.5-t)/4.5 + (9-t)/9]/2
Solving gives t = 3 hours, at which time the candles will have heights of 1/3, 1/2, and 2/3, making a nice line.
Good luck getting your 3*-year old to wait 3 hours to blow out the candle.
*hint, hint, hint