Ask Question
16 November, 00:58

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?

+1
Answers (1)
  1. 16 November, 04:52
    0
    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)
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “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 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers