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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 RSR_S be Sandra's rate and RFR_F be Frederick's rate.

From the given, Sandra's rate is:

RS=3 sandcastles5 hours(1)R_S=\dfrac{3\text{ sandcastles}}{5\text{ hours}}\color{white}{\tag{1}}

RS=35sandcastleshrR_S=\dfrac{3}{5}\dfrac{\text{sandcastles}}{\text{hr}}

Together, their rate is:

RT=3 sandcastles3 hoursR_T=\dfrac{3\text{ sandcastles}}{3\text{ hours}}

RT=1sandcastlehrR_T=1\dfrac{\text{sandcastle}}{\text{hr}}

Hence,

RS+RF=RTR_S+R_F=R_T

35+RF=1\dfrac{3}{5}+R_F=1

RF=135R_F=1-\dfrac{3}{5}

RF=5535R_F=\dfrac{5}{5}-\dfrac{3}{5}

RF=25sandcastlehr\color{#c34632}{R_F=\dfrac{2}{5}\dfrac{\text{sandcastle}}{\text{hr}}}

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