Water boils at different temperatures at different elevations. The boiling temperature of water is 212F at sea level​ (0 feet) but drops about 1.72F for every​ 1,000 feet of elevation.

Question

Water boils at different temperatures at different elevations. The boiling temperature of water is 212°F at sea level​ (0 feet) but drops about 1.72°F for every​ 1,000 feet of elevation. Write a formula for the boiling point at a given elevation. Then solve the formula for the elevation when the boiling point for water is 190°F.

Part A-

Determine a formula for the boiling point​ b, in degrees​ Fahrenheit, at elevation​ h, in feet.

Part B-

When the boiling point is 190°​F, the elevation is about ___ ft.

Answer 1

This is a linear relationship. Let x = the altitude in feet and y be the boiling point.

A)

For a linear equation, we want y = mx+b

From the description m = -1.72/1000 and when x = 0, y = 212, so b = 212

y = -1.72/1000 + 212

B) When y = 190

190 = -1.72/1000x + 212

1.72x/1000 = 22

x = 22000/1.72 ≈ 12791 feet

When the boiling point is 190°​F, the elevation is about 12791 ft.