Clarence works at a coal mine 8 hours a day except for Friday where he works 9 hours, and his weekly job quota is to obtain 196 pieces of coal.
Clarence, on average, finds 4 pieces of coal every hour, but can only mine at a pace of 3 pieces of coal per hour; He will, however, work overtime in order to mine pieces of coal that he originally didn't get to but had found beforehand.
How many hours (rounded to the nearest quarter) will it take for Clarence to meet his quota and does he meet his quota?
I'm assuming a 5-day work week...
The number of hours he works per week = 4(8) + 9 = 41 hrs
If he mines 3 pieces per hour.....he mines 41(3) = 123 pieces mined per week
And he has left to be mined = 41 pieces
And it will take him 41/3 ≈ 13 + 2/3 overtime hours to mine all the coal he has found
So he mines 41(4) = 164 pieces in 41 + 13 + 2/3 = 54 + 2/3 hours
Note that it will take him 196/3 ≈ 65 + 1/3 hours to meet his quota if he only mines 3 pieces per hour....thus....he cannot meet his quota, even with the overtime hours