The boiling point of a liquid decreases with decreased pressure. Since air pressure is lower in the mountains, water will boil at a lower temperature than it does at sea level. This means that it requires less energy and therefore a shorter heating time to reach its boiling temperature. Air pressure is caused by the weight of the atmosphere above us. The higher the altitude, the less air above us so the lower the pressure.

The boiling point of a liquid is the temperature at which the vapor pressure of the liquid equals atmospheric pressure. The vapor pressure, which is the pressure exerted by gaseous molecules of the substance at its surface, increases with temperature. Water’s vapor pressure reaches 760 mm Hg at a temperature of 100 C, its normal boiling point. This is the normal pressure at sea level. If the atmospheric pressure is less than 760 mmHg the vapor pressure of water will reach the atmospheric pressure and boil at a lower temperature.

Cooking directions are often altered for high altitudes because the lower boiling temperature of water results in slower cooking.

Why does water boil faster on the top of a mountain?

Water boils at a lower temperature (therefore faster) at high altitudes because the atmospheric pressure it lower. A liquid will begin to boil when its vapor pressure equals atmospheric pressure. The vapor pressure of water increases with temperature. The normal boiling point, 100 degrees C or 373K, is the temperature at which the vapor pressure equals 1.00 atm pressure, the normal pressure at sea level. 

Atmospheric pressure decreases with altitude because the weight of the air above decreases.

When the atmospheric pressure is lower, the vapor pressure of water will reach atmospheric pressure at a lower temperature. We might say that the water boils "faster" because it reaches boiling at a lower temperature, but at the lower temperature it will cook food more slowly.

At pressures higher than atmospheric pressure the boiling point of water is higher. A pressure cooker reduces cooking time by keeping water in the liquid phase at temperatures above 100 degrees C.

Will water boil faster at sea level or on top of a hill or mountain?

According to Bodner Research Web that is produced by Perdue University, a liquid boils when its vapor pressure is equal to the pressure that is exerted on the liquid by its environment. It is then that bubbles form inside the liquid.

Pressure is caused by the bombardment or collision of particles with a surface. As one moves up a mountain or hill, the number of air particles decreases. Therefore, there is less pressure as the elevation increases up a hill or mountain.

Since the air pressure is less, the water molecules on top of a mountain or hill are not “squished” together as much as they would be at sea level. Therefore, the water is able to expand with greater ease and boil faster at the higher elevation. Thus, at higher elevations, water boils at a lower temperature. For this reason, the amount of cooking time or the temperature at which a food is cooked may need to be increased when made at higher elevation.