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Question

# Sandra could build 3 sandcastles in 5 hours. Working with Frederick, she discovered they could build 3 sandcastles in merely 3 hours. What was Frederick's rate of building sandcastles?

Solution

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Let $R_S$ be Sandra's rate and $R_F$ be Frederick's rate.

From the given, Sandra's rate is:

$R_S=\dfrac{3\text{ sandcastles}}{5\text{ hours}}\color{white}{\tag{1}}$

$R_S=\dfrac{3}{5}\dfrac{\text{sandcastles}}{\text{hr}}$

Together, their rate is:

$R_T=\dfrac{3\text{ sandcastles}}{3\text{ hours}}$

$R_T=1\dfrac{\text{sandcastle}}{\text{hr}}$

Hence,

$R_S+R_F=R_T$

$\dfrac{3}{5}+R_F=1$

$R_F=1-\dfrac{3}{5}$

$R_F=\dfrac{5}{5}-\dfrac{3}{5}$

$\color{#c34632}{R_F=\dfrac{2}{5}\dfrac{\text{sandcastle}}{\text{hr}}}$

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