Shiloh wants to buy a long lasting candle. Type 1 candle melts by 19.5 cm each hour. Type 2 candle melts by 0.15 inch each minute. Both the candles have the same original height.
[1 inch = 2.54 cm]

Part A: Which type of candle should Shiloh buy? Justify your answer by comparing the rate at which they melt after converting to the same units.

Part B: If the original height of the candles was 40 cm and you checked on its height every 30 minutes after lighting it, describe appropriate scales on the x-axis and y-axis to graph the rate at which the slower candle melts.

Question

Shiloh wants to buy a long lasting candle. Type 1 candle melts by 19.5 cm each hour. Type 2 candle melts by 0.15 inch each minute. Both the candles have the same original height.
[1 inch = 2.54 cm]

Part A: Which type of candle should Shiloh buy? Justify your answer by comparing the rate at which they melt after converting to the same units.

Part B: If the original height of the candles was 40 cm and you checked on its height every 30 minutes after lighting it, describe appropriate scales on the x-axis and y-axis to graph the rate at which the slower candle melts.

yanasidlinskiy · Answer

candle 1's rate: 19.5 cm/hr 
candle 2's rate: 0.15 in/min 

1 inch = 2.54 cm 
0.15 in = 0.15x2.54 = 0.381 cm 

candle 2's converted rate = 0.381 cm/min 
60 min = 1 hr 
0.381 cm/min = 0.381x60 cm/hr = 22.86 cm/hr 

compare: 
Candle 1 @ 19.5 cm/hr 
Candle 2 @ 22.86 cm/hr 
===> Candle 1 melts more slowly so would be the preferred choice 

Part B: 
x-axis would be time, and each unit on the axis would be appropriate at 30 min. 
y-axis would be height, with each unit being, perhaps, 4 cm so candle would start at (0,10).