The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire and inversely proportional to the cube of his distance from the fire. If the hiker is 22 ft from the fire and someone doubles the amount of wood burning, how far from the fire would he have to be so that he feels the same heat as before?

Question

Mathematics

Alma Choi

1 December, 18:07

The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire and inversely proportional to the cube of his distance from the fire. If the hiker is 22 ft from the fire and someone doubles the amount of wood burning, how far from the fire would he have to be so that he feels the same heat as before?

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Answers (1)

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Mallory Mays · Answer 1

28 feet

Step-by-step explanation:

Heat, H = (k X Amount of Wood) / Distance³

H = (kW) / d³ where k is proportionality constant.

Let Amount of Wood be W

Distance=22 feet

H=kXW/22³

H=kW/10648 ... (1)

If the amount of Wood (W) is doubled, and the heat is to remain the same.

Amount of Wood=2W

H = (2Wk) / d³ ... (2)

Equating (1) and (2)

kW/10648 = (2Wk) / d³

Cross multiplying

kWd³ = 10648 X 2Wk

Dividing all through by Wk

d³ = 21296

Taking cube roots of both sides

d=27.71826309769

d=28 feet (to the nearest whole number)