In right pyramid PABCD, ABCD is a square with sides of length 2 and the distance from P to the center of square ABCD is 1. A plane intersects the pyramid at A and intersects edges PB, PC and PD at points B', C' and D', respectively. If and , what is the value of the ratio ? Express your answer as a common fraction.
Ojns is robbing some gold! He brings a kg briefcase which has volume cm by cm by cm. If he can lift a maximum of kg, and he plans on filling up the whole case, could he lift it? If not, what is the maximum number of bars of gold, each measuring cm by cm by cm, should he put in the case so he can lift it?
Billy can mow a lawn in 6 hours and paint a roof in 2 hours. Joel can mow a lawn in 8 hours and paint a roof in 4 hours. Elton can mow a lawn in 4 hours and paint a roof in 4 hours.
Billy and Elton begin painting the roof while Joel begins mowing the lawn. When Billy and Elton finish painting the roof, Elton goes inside to play the piano while Billy helps Joel finish mowing the lawn. How long will it take to do both paint the roof and mow the lawn?