VJesus12 wrote:One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 5 robots altogether, if the robots build only one robot at a time?
A. 70 min
B. 94 min
C. 110 min
D. 112 min
E. 120 min
Let each robot = 2 units.
Since a faster robot takes 1 hour to produce a 2-unit robot, the rate for a faster robot = w/t = 2/1 = 2 units per hour.
Since a slower robot takes 1 hour to produce a 2-unit robot, the rate for a slower robot = w/t = 2/2 = 1 unit per hour.
Each additional robot produced takes 2 hours to produce a 2-unit robot.
Thus, each additional robot produced is a SLOWER ROBOT with a rate of 1 unit per hour.
Time for the first 2 robots to produce a third 2-unit robot = w/(combined rate for 1 faster and 1 slower robot) = 2/(2+1) = 2/3 hour = 40 minutes.
Time for the resulting 3 robots to produce a fourth 2-unit robot = w/(combined rate for 1 faster and 2 slower robots) = 2/(2+1+1) = 1/2 hour = 30 minutes.
Time for the resulting 4 robots to produce a fifth 2-unit robot = w/(combined rate for 1 faster and 3 slower robots) = 2/(2+1+1+1) = 2/5 hour = 24 minutes.
Total time for there to be 5 robots = 40+30+24 = 94 minutes.
The correct answer is
B.
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