Spruce planting

Mrs. Brown planted 50 spruce trees in three and a half hours in the morning. Mrs. Clark came in the afternoon, and together they planted another 100 spruce trees in four and a half hours.

Find:
A. How long would it take Mrs. Clark to plant 50 spruce trees by herself?
B. How many spruce trees did Mrs. Clark plant during the afternoon?

Final Answer:

a =  6.3 h
b =  35

Step-by-step explanation:

$$\begin{gathered} t_1=3+1/2=\frac{7}{2}=3.5 \\ {t}_2=4+1/2=\frac{9}{2}=4.5 \\ V=50/t_1=50/3.5=\frac{100}{7}\doteq 14.2857 \\ K=(100-t_2\cdot V)/t_2=(100-4.5\cdot 14.2857)/4.5=\frac{500}{63}\doteq 7.9365 \\ a=50/K=50/7.9365=\frac{63}{10}\text{h}=6.3\text{h} \end{gathered}$$

$b=\lfloor K\cdot t_2\rfloor =\lfloor 7.9365\cdot 4.5\rfloor =35$

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