If the candles when new were each 'h' inches high, we know that one burns at the rate of h/4 inches per hour and the other at h/5 inches per hour. Suppose that after the peal, 'x' inches are left of one and '4x' inches of the other. This means that (h - x) inches of one and (h - 4x) inches of the other burnt away in the same time.

Hence:-

So 16x = h, therefore x=1/16 of the length of one candle which is 1/4 hour of burning time of this candle. The candle has been alight for 3 3/4 hours. (This figure can be double checked by using the figures for the second candle).