# RATL 2 | Lesson 4 | Practice (Rate Problems) Solutions

Solutions

1. Anna and Carlos need to make the dinners. Bill and Dianne need to make the desserts.
2. Anna and Carlos can each make 30 dinners in an hour.

\begin{align} \dfrac{30}{180}+\dfrac{30}{180}&= \dfrac{1}{t} \\\\ \dfrac{1}{6}+\dfrac{1}{6} &= \dfrac{1}{t} \\\\ t+t &= 6 \\\\ t &= 3 \end{align}

It will take Anna and Carlos 3 hours to make all the dinners.

Bill can make 40 desserts in an hour. Dianne can make 60 desserts in an hour.

\begin{align} \dfrac{40}{180}+\dfrac{60}{180}&= \dfrac{1}{t} \\\\ 2t+3t &= 9 \\\\ 5t &= 9 \\\\ t &= 1\dfrac45 \end{align}

It will take Bill and Dianne 1 hour and 48 minutes to make all of the desserts. When they are done, they can help with the dinners.