A man can begin a work at his maximum rate, but afterwards the rate at which he works follows a cyclic pattern. Every two hours, it reduces by half but after 8 hours, it comes back to its maximum level. He can complete a job in 151 hours at his maximum level. He can complete a job in 151 hours at his maximum rate. How many hours would he take to complete the job if his rate follows the cyclic pattern

Question

A man can begin a work at his maximum rate,  but afterwards the rate at which he works follows a cyclic pattern. Every two hours, it reduces by half but after 8 hours, it comes back to its maximum level. He can complete a job in 151 hours at his maximum level.  He can complete a job in 151 hours at his maximum rate. How many hours would he take to complete the job if his rate follows the cyclic pattern

oobleck · Answer

in 2 hours, he completes 2/151 of the job
in the next 8 hours, he completes 4/151 of the job.
So, after 10 hours, he has done 6/151 of the job
In 25*10 = 250 hours, he has done 150/151 of the job.
So it will take him 251 hours