Question

An overzealous student burns a candle at both ends. One night she lights the top and bottom ends of a candle at the same time. The candle is cylindrical: 10 inches long and with a radius of 0.5 inches.. If the top flame burns down at 1.4 inches per hour and the bottom lame burns up at a rate of 2.1 inches per hour,

A: How far from the top do the flames meet?
B: how can she get the flames to meet up in the middle of the candle by lighting the ends at different times?

Answer 1

A. the distance covered by both ends = top distance+bottom distance

1.4 inches + 2.1 inches =3.5 inches

so each hour, both ends cover 3.5 inches

he time it'll take to burn the whole candle

10 inches/ 3.5 inches =2.857 hours

to find out how far from the top the flames meet,

1.4 inches x 2.854 hours = 4 inches

B. the middle of the candle is 10/2 = 5 inches

to meet at the middle, she should start

Top: 1.4 inches × x hours = 5 inches

x hours = 5/1.4 = 3.571 hours

Bottom : 2.1 inches × x hours = 5 inches

x hours = 5/2.1 = 2.38 hours

Answer 2

A. the distance covered by both ends = top distance+bottom distance

1.4 inches + 2.1 inches =3.5 inches

so each hour, both ends cover 3.5 inches

he time it'll take to burn the whole candle

10 inches/ 3.5 inches =2.857 hours

to find out how far from the top the flames meet,

1.4 inches x 2.854 hours = 4 inches

B. the middle of the candle is 10/2 = 5 inches

to meet at the middle, she should start

Top: 1.4 inches × x hours = 5 inches

x hours = 5/1.4 = 3.571 hours

Bottom : 2.1 inches × x hours = 5 inches

x hours = 5/2.1 = 2.38 hours