From the exercise, we know that it takes Susan

2

hours to paint her living room. If we call the area of the room's walls

A,

then Susan's speed per hour can be expressed as the area divided by the number of hours it takes her to paint the walls.

Susan ’ s speed = \frac{A}{2}

Similarly, Jaime's speed per hour can be expressed as the ratio of the wall's area divided by the number of hours it takes him to paint the room.

Jaime ’ s speed = \frac{A}{3}

If we add the speed of Susan and Jaime, we can determine their combined speed.

\frac{A}{2} + \frac{A}{3}

$\frac{a}{b} = \frac{a \cdot 3}{b \cdot 3}$

\frac{3 A}{6} + \frac{A}{3}

$\frac{a}{b} = \frac{a \cdot 2}{b \cdot 2}$

\frac{3 A}{6} + \frac{2 A}{6}

Add fractions

\frac{5 A}{6}

Now we can determine the time

t

that it takes for them to paint the room together by equating the product of the time and speed with the area of the room.

\frac{5 A}{6} \cdot t = A

$LHS \cdot 6 = RHS \cdot 6$

5 A \cdot t = 6 A

$LHS / 5 A = RHS / 5 A$

t = \frac{6 A}{5 A}

Use a calculator

t = 1.2

It is going to take

1.2

hours to paint the room if they work together.

Exercise 76 Page 611

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