math
posted by Tia .
Rodney and James are each 30 feet from a door. Rodney moved one foot closer and James moved half the distant between himself and the door. If each person continued to move in this fashion, who would be closer to the door after 10 moves? Who reaches the door first?

In 10 moves, Rodney has covered 10 feet , so he is 20 ft from the door
in 10 moves , James has moved:
15 + 15/2 + 15/4 + 15/8 + 15/16 + .. + 15/2^9
this is a geometric series with a= 15, r = 1/2
sum(10) = 15(1  (1/2)^10)/(1  1/2)
= (1023/1024)(30)
so he is (1/1024)(30) feet away from the door
notice on the 10th move, he is 1/2^10 of the distance away.
moving in this fashion , James will never get to the door
e.g., after 1000 moves he would still be (1/2^1000) of the distance away from the door
whereas Rodney will clearly reach the door after 30 moves.
Respond to this Question
Similar Questions

math 4th grade question
Rodney is 3 times as old as his sister.A year ago, he was 4 times as old. How oldare Rodney and his sister now? 
Math
I need help with this questions. a). An overhead garage door has two springs, one on each side of the door. A force of 15 pounds is required to stretch each spring 1 foot. Because of a pulley system, the springs stretch only onehalf … 
physics
A uniform beam of length 7.60 m and weight 3.90 102 N is carried by two workers, Sam and Joe, Sam=1.00m Joe=2.00m between both Joe and Sam there is 7.60m (a) Determine the forces that each person exerts on the beam. F_Sam = N F_Joe … 
Math
Henry is building a front door. The height of the door is one foot more than twice its width. If the door is seven feet high, what is its width? 
Selam
A real object is placed in front of a diverging lens, at a distance less than the focal length. When the object is moved slightly closer to the lens, which direction does the image move? 
Algebra
If Patrick walked one mile in an hour and a half and Rodney walked the same mile in an hour, how much faster was Rodney walking than Patrick? 
math
Rodney and Cauls’s houses having distance of eleven km Rodney start from his house by walking at the speed of 6 km / hr , Caouls at 5 km / hr at what distane they will meet , if Rodney start his journey later by 5 minutes then which … 
math
Rodney and Cauls’s houses having distance of eleven km Rodney start from his house by walking at the speed of 6 km / hr , Caouls at 5 km / hr at what distane they will meet , if Rodney start his journey later by 5 minutes then which … 
English
1. Lock the door. 2. Lock the door, will you? 
ap physics
Suppose that a person closes a car door. The person's fingers are in the door opening, that is located 0.50 m from the hinges. The rotational inertia of the car door is 5.0 kg⋅m2. The door closes in 0.1 s and the rotational speed …