Grandmother's 69254

The grandmother and granddaughter Julia harvest currants in 15 hours of work together. Julia would harvest currants for ten days after 6 hours of work a day.
a) Determine in hours how long the harvest would have taken for her grandmother if Julča had not helped her.
b) Determine the percentage by which the grandmother's harvest time was reduced when her granddaughter was involved in the harvest.

Correct answer:

B =  20 h
p =  25 %

Step-by-step explanation:

$$\begin{gathered} J=10\cdot 6=60\text{h} \\ S=15 \\ S\cdot (1/B+1/J)=1 \\ S\cdot (1+B/J)=B \\ 15\cdot (1+B/60)=B \\ 45B=900 \\ B=\frac{900}{45}=20 \\ B=20=20\text{h} \end{gathered}$$

$p=100\cdot \frac{B-S}{B}=100\cdot \frac{20-15}{20}=25\%$

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