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

MATH152 April 2017
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### Question B 01 (a)

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).

 Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!