Rate Concept (Candle)

First
Two candles of the same height are lit at the same time. The first candle takes 5h to burn completely. The second candle takes 4h to burn completely. If each candle burns at a constant rate, how long does it take, in hours, for the height of the first candle to be four times that of the second candle?

Part I
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Method 1: (Common Total Concept)
1st Candle (Rate) = 1/5 candle/hour = 4/20 candle/hour
2nd Candle (Rate) = 1/4 candle/hour = 5/20 candle/hour

(Amount Burnt)1st Candle : 2nd Candle
= 4u : 5u

Method 2: (Inverse Proportionality + Proportionality Concept)

(Time)
1st Candle : 2nd Candle
= 5 : 4

(Rate)
1st Candle : 2nd Candle
= 4 : 5

(Amount Burnt)
1st Candle : 2nd Candle
= 4u : 5u

Part II
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(Remaining Amount)
1st Candle : 2nd Candle
= 4p : 1p

Method 1: Elimination  and Substitution Concept

(Full Candle): 4u + 4p = 5u + 1p

(Elimination): 3p = 1u  or 1u = 3p

(Expansion): 4u = 12p

(Substitution) 
Total Candle = 4u + 4p = 12p + 4p = 16p

(Amount Burnt)1st Candle = 4u = 12p

12/16 x 5 hours = 3 3/4 hours = 3.75 hours = 3 hours 45 minutes

Method 2: Bar Model Drawing


1st Candle: 
 U   U   U   U PPP P
 U   U   U   U   U  P
2nd Candle:

1st Candle: 
PPP PPP PPP PPP PPP P
PPP PPP PPP PPP PPP P
2nd Candle:

12/16 x 5 hours = 3 hours 45 minutes