Krugen K.

asked • 10/14/21

Work time math help

There are three groups, Group A has 6 efficient workers who can get a work done in 10 days. Group B has 8 moderately skilled workers who can get the same work done in 12 days. Group C has 10 low-skilled workers who can get the same work done in 15 days. Nine (9) workers are chosen, 2 from Group A, 5 from Group B and 2 from Group C. In how many days can these nine (9) workers get the job done? (please show all steps involved).

Dennis C.

There are multiple ways to skin this work rate problem. However, the most straight forward method is to determine the rate for each worker and then use that to calculate the combined rate of the 9 workers selected. Group A - 6 workers can complete the job in 10 days. That means there will a total of 60 person days needed for this job (at the rate of these workers). Each worker then, completes 1/60 of the job each day. The rate for a Group A worker is 1/60. Group B - 8 workers can complete the job in 12 days. So, 96 total hours to complete and the Group B worker rate is 1/96. Group C - 10 workers can complete the job in 15 days. So, 150 total hours to complete yielding a Group C worker rate of 1/150. Now, we select 2 workers from Group A, 5 from Group B and 2 from Group C. Numerically, we can show the total amount of the job completed in a single day by summing their respective worker rates: 1/60 + 1/60 + 1/96 + 1/96 + 1/96 + 1/96 + 1/96 + 1/150 + 1/150, or 2/60 + 5/96 + 2/150. Adding fractions requires determining a common denominator, and using the Lowest Common Multiple rule we find that 2400 is the LCM. Now, we have: 80/2400 + 125/2400 + 32/2400 = 237/2400 At this point, we can estimate the answer to be a bit more than 10 (237 x10 = 2370). 10 30/2400, or 10 3/240, or 10 1/80.
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11/30/21

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