The amount of time that three people worked on a special project was in the ratio of 2 to 3 to 5. If the project took 110 hours, what is the difference between the number of hours worked by the person who worked for the longest time and the person who worked for the shortest time ?

11

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22

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33

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14

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Solution

The correct option is B $33$
33 hours: Use an equation with the unknown multiplier to represent the total hours put in by the three people:
$2 x + 3 x + 5 x = 110$
$10 x = 110$
$x = 11$
Therefore, the person who worked for the longest time put in 5(11) = 55 hours, and the person who worked for the shortest time put in 2(11) = 22 hours. This represents a difference of $55 - 22 = 33$ hours.

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