Jake worked 12 more overtime hours than Smith one week. If Jake worked 8 overtime hours for every 6 overtime hours that Smith worked, for how many hours of overtime did each person work? Round your answer to the nearest tenth of an hour if necessary. Answer must include unit of measure.
To solve this problem, let's assign variables to the unknowns.
Let's say that the number of overtime hours Smith worked is S.
According to the problem, Jake worked 12 more overtime hours than Smith, so we can say that Jake worked S + 12 overtime hours.
It is also given that Jake worked 8 overtime hours for every 6 overtime hours that Smith worked. So, we can set up the equation:
(S + 12) / S = 8 / 6
To solve for S, we can cross-multiply:
6(S + 12) = 8S
Distribute the 6:
6S + 72 = 8S
Subtract 6S from both sides:
72 = 2S
Divide both sides by 2:
36 = S
So, Smith worked 36 overtime hours.
To find Jake's overtime hours, we can substitute S back into the equation:
Jake's overtime hours = S + 12 = 36 + 12 = 48
Therefore, Smith worked 36 overtime hours and Jake worked 48 overtime hours.