# Science:Math Exam Resources/Courses/MATH152/April 2017/Question B 01 (a)/Statement

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Three engineering students, Xiuying, Arjan, and Marianne decide to take a summer job painting homes. Xiuying paints three times as fast as Marianne and twice as fast as Arjan and Marianne combined. All three together paint a room in four hours.

(a) [2 marks] Let ${\displaystyle x=(x_{1},x_{2},x_{3})^{T}}$ be the vector, where ${\displaystyle x_{1}}$, ${\displaystyle x_{2}}$ and ${\displaystyle x_{3}}$ are respectively the number of rooms that Xiuying, Arjan, and Marianne can paint in an hour. Describe the information above as a linear system in the form

${\displaystyle Ax=b}$

(write ${\displaystyle A}$ and ${\displaystyle b}$ with specific values).