Early mountaineers used boiling water to estimate the height

Early mountaineers used boiling water to estimate the height of the mountains they climbed. If they reached a given peak and found that water boiled at 120 degrees F instead of 212 degrees F at sea level, approximately how high (ft) was this mountain? Show all steps.

Solution

At sea level, water boils at 212 °F. With each 500-feet increase in elevation, the boiling point of water is lowered by just under 1 °F. Total reduction in boiling point=212-120=92^oF

Let height of mountain be h

h/500=92

h=92*500=46000 ft

Therefore, height of mountain is approximately 46000 ft