Four prospectors with only one lantern must walk through a mineshaft. At most, two prospectors can travel together and any prospector in the shaft must be with the lantern.The prospectors, named Andrews, Blake, Johnson, and Kelly, can walk through the shaft in one minute, two minutes, four minutes, and eight minutes, respectively. When two walk together they travel at the speed of the slower prospector. How can the prospectors get through the mineshaft in only 15 minutes? After you have solved this problem, explain how you got your foot in the door.