Question

	Widgets	Hours	Breaks
Rishi	28	4	2
Dillyn	42	6	4
Shane	27	5	2

Rishi, Shane, and Dillyn work at a widget factory. The table above shows the number of hours they each spent at the factory on a given day, the number of widgets they produced, and the number of 15-minute breaks they took while they were at the factory. Each man works at a constant rate.
Rishi and Shane are each assigned an equal number of widgets. Neither will take breaks in order to complete this assignment as quickly as possible. I order that they both finish the assignment at the same time , Rishi offers to do a certain percentage of Shane's assignment. What percentage of Shane's original assignment does Rishi do?

• A. $12.5\%$
• B. $14.3\%$
• C. $16.7\%$
• D. $25\%$

Answer 1

The correct option is B $14.3\%$

First, solve for Rick's hourly rate and Shane's hourly rate. Since Work =Rate x Time, Rick produces $8$ widgets per hour ($28$ widgets divided by $3.5$ hours without breaks) and Shane produces $27÷3.5$ = $6$ widgets per hour.
Now plug in. Since you know they have a combined rate of $14$ widgets per hour, choose a total amount that is divisible by $14$.
Let's say they were each assigned $14$. This means that the total produced is $28$, and at a total rate of $14$ per hour. Therefore, it takes them $2$ hours to finish.
During this time Rick would produce $16$ widgets and Shane would produce $12$ widgets. Therefore, Rick must have done $2$ of Shane's originally assigned $14$ widgets, which is $14.3$%.
Option B is correct.