candle is lit and after 10 minutes, it is also lit at the other end . 20 minutes later,the candle is completely melted . if the candle were lit at both the ends to begin with,and then one end were extinguished when only half of the candle remained, how long in total would it take for the candle to completely melt?
Answers
Answer:
Time taken to melt the candle completely = 37.5 min
Step-by-step explanation:
In 1st case, the candle is lit from one end for 10 mins, and 20 mins from both ends.
When lit from 2 ends, the speed will be double.
∴20 mins lit from 2 ends = (20 + 20) mins lit from one end.
∴ to melt the candle completely only from one end lit, time taken = 10 + 20 + 20
∴ Time taken to melt from single end = 50 mins
If the length of candle = X,
speed of melting from single end = X/50 units/min ...(1)
∴ Speed of melting from 2 ends = 2 × X/50 = X/25 units/min ...(2)
Candle is lit from both ends, till candle became half.
∴ Time taken = Length of candle melted ÷ Speed (2 side melting)
∴ Time taken T1 = (X/2) ÷ (X/25)
∴ T1 = 12.5 min ...(3)
For the rest of the hlaf, only one end is lit and other is extinguished.
∴ Time taken T2 = Length of candle melted ÷ Speed (single side)
∴ T2 = (X/2) ÷ (X/50)
∴ T2 = 25 min
∴ Total time taken to melt the candle completely T = T1 + T2
∴ T = 12.5 + 25
∴ T = 37.5 mins