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# Barry and the ice cream delimma

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Barry runs an ice-cream shop and has 5 identical ice-cream-bar making machines,which he usually starts running at 7:00am so he would finish making all ice-creambars for the day at 9:00am. However, due to a power glitch at 7:18am, two of the ice-cream machines stopped working, though thankfully nothing turned bad.The power came back on at 7:25am (no ice-cream was made between 7:18am and 7:25am), and Barry still needs to make the exact same number of ice-creams, as the delivery truck is still coming to pick up the ice-cream bars. He must now find out the time when the machines would finish making all ice-cream bars for the day. Can you help him? Please answer in the format XX:YY, where XX is the hour, and YY isthe minute.

Jan 10, 2021

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Each machine  completes   1/10  of the  total work in 1 hour

3  work the whole  2 hours....so....they complete   2(1/10)*3 =  6/10 of the work during this time

The other two  work one  whole  hour  (between 8 and 9)  without stopping so they complete another  1 (1/10) * 2  = 2/10  of the work  during this time

So......we  have accounted for  8/10  of the work

Between  7  and 8   the other two machines  complete  (53/60) * 2 (1/10)  =  53/300  more of the work

So....the  five machines complete    8/10 + 53/300  =    293/300    of the work in two hours

So....the five must   complete     7/300  of the remaining work after 9 AM

Note that each minute.....one machine  completes (1/10) (1/60)   =  1/600  of the work

So..... each minute  the   5  machines complete   5/600  =  1/120  of the work

So....the  number of additional  minutes they  must  work  to  complete the job is

Work remaining /  portion of  work done each minute  =

(7/300)  /( 1/120) =   (7/300) (120) =  14/5 =   2.8 minutes  =   2 min  48 sec

So....the time  for completion is  9 AM + 2min 48 sec =     9:02:48

Jan 10, 2021