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.

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

Answer 1

Since the boiling temperature is decreasing at a steady rate, we can use the typical y = mx + b formula

In this case, our independent variable would be height, h, since that's the number we can play around with. It will replace the x in the formula.

The rate of decrease they give us if per 1000 feet, so in order to find the rate per 1 foot, just divide by 1000: -1.72/1000. That is our m. Since the temperature is decreasing, the rate is negative.

Our b can be found by knowing the boiling temperature at sea level, 212F

Putting that all together, our final formula would be b = (-1.72/1000)*h + 212.

Note: The b in the original equation represents the y-intercept and is standard notation for that formula. It is not the same as the b in the final formula, which represents the new boiling temperature at height h.

Using that information, we can find the height corresponding to a boiling temperature of 190 = b

190 = (-1.72/1000)*h + 212

We're trying to isolate the h, so subtract 212:

-22 = (-1.72/1000)*h

Get rid of the fraction:

-22(-1000/1.72) = h

Simplify:

h = 22(1000/1.72) ≈ 12790 ft

Answer 2

B = 212 - 1.72*E, where E is 1000's of feet of elevation

Given B = 190

190 = 212 - 1.72*E

-22 = -1.72*E

12.8 = E in 1000's of feet

so elevation is 12.8 * 1000 = 12800 feet.