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 8 robots altogether, if the robots build only one robot at a time?
Pick one
A) 70 min  B) 94 min  C) 110 min  D) 131 1/7 min  E) 146 1/7 min
First the 2 robots work at the rate of   1 + 1/2 = 3/2   so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)   Now the 3 robots work together at the rate of   1 + 1/2 + 1/2 = 4/2= 
<gadget id="calculator">4/2</gadget>
<output>2</output>
2/1   so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)   Now the 4 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2= 5/2   so they complete one robot in 2/5th of an hour - (3)   Now the 5 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2+1/2= 
<gadget id="calculator">1 + 1/2 + 1/2 + 1/2+1/2</gadget>
<output>3</output>
3   so they complete one robot in 1/3th of an hour - (4)   Now the 6 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2   so they complete one robot in 2/7th of an hour - (5)   Now the 7 robots work together at the rate of   1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=9/2   so they complete one robot in 2/9th of an hour - (6)   And now we have 8 robots   So Total = (1) + (2) + (3)+(4)+(5) + (6) = 146 1/7minutes   Answer - 146 1/7 min
<result>E</result>
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 8 robots altogether, if the robots build only one robot at a time?