Jewellery-maker

A jewellery-maker threads 5 beads in 20 seconds. A necklace consists of 210 beads, 30 are already threaded.
a) Write an equation of the dependence of the number of threaded beads on time (in minutes), during which the jewellery-maker will be threading the beads.
b) In what time will the jewellery-maker finish the entire necklace?
c) In what time will the jewellery-maker thread 30 necklaces if she would not have a single bead threaded?
Write as an equation and express the time in hours.

Final Answer:

f = 15t
t₁ =  12 min
t₃ =  7 h

Step-by-step explanation:

$$\begin{gathered} f=\frac{5}{20}\cdot 60t \\ r=\frac{5}{20}\cdot 60=\frac{5\cdot 60}{20}=\frac{300}{20}=15 \\ f=r\cdot t \\ f=15t \end{gathered}$$

$t_1=\frac{210-30}{r}=\frac{210-30}{15}=12\text{min}$

$$\begin{gathered} n=30 \\ {t}_2=\frac{210\cdot n}{r}=\frac{210\cdot 30}{15}=420\text{min} \\ {t}_3=t_2\to \text{h}=t_2:60\text{h}=420:60\text{h}=7\text{h}=7\text{h} \end{gathered}$$

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