Princesses

Princesses Anna and Elsa are picking strawberries, which have ripened in huge quantities after a long winter. Anna can pick one bed in 120 minutes, and Elsa is faster and can finish an equally large bed in 15 minutes. How many minutes would it take the royal sisters to pick the same bed of strawberries if they picked together?

Final Answer:

t =  56 min

Step-by-step explanation:

$$\begin{gathered} t_1=120\text{min} \\ {t}_2=t_1-15=120-15=105\text{min} \\ m=\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{120}+\frac{1}{105}=\frac{7}{840}+\frac{8}{840}=\frac{7+8}{840}=\frac{15}{840}=\frac{1}{56}\doteq 0.0179 \\ t\cdot m=1 \\ t=1/m=1/0.0179=56\text{min} \end{gathered}$$

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