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kati45 [8]
3 years ago
5

Two groups of staff at a store are making flowers to decorate the entrance. If Group A were to do it alone, it would take them 1

0 hours to complete the task. If Group B were to do it alone it would take them 15 hours. The groups decided to work together. Group B took a break for 1 hour and 40 minutes. Group A ended up making 300 more flowers than Group B. HOW MANY FLOWERS ARE THERE ALTOGETHER?
Mathematics
1 answer:
Tcecarenko [31]3 years ago
6 0

Answer:

\dfrac{6750}{7}

Step-by-step explanation:

Let x be the number of flowers. If Group A were to make x flowers alone, it would take them 10 hours to complete the task, then they make \dfrac{x}{10} flowers in an hour.  If Group B were to make x flowers alone, it would take them 15 hours to complete the task, then they make \dfrac{x}{15} flowers in an hour.

The groups decided to work together. They can make \dfrac{x}{10}+\dfrac{x}{15}=\dfrac{x}{6} together in an hour and it takes them \dfrac{x}{\frac{x}{6}}=6 hours. Group B took a break for 1 hour and 40 minutes (1\dfrac{2}{3} hour), then Group B works

6-1\dfrac{2}{3}=4\dfrac{1}{3} hours.

Thus,

\dfrac{x}{10}\cdot 6-\dfrac{x}{15}\cdot 4\dfrac{1}{3}=300,\\ \\\dfrac{3x}{5}-\dfrac{13x}{45}=300,\\ \\14x=300\cdot 45=13500,\\ \\x=\dfrac{13500}{14}=\dfrac{6750}{7}.

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