a 20cm candle has wick at each end.if each end is lit, the lower flame burns at a rate of 9 cm/hr and the upper flame burns at a rate of 6 cm/hr, how long will it take for the flames to meet?

Not a very realistic question, but it can be solved mathematically.

let the time taken be t hrs.
9t + 6t = 20
t = 20/15 hrs or 80 minutes.