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 10 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?

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 [tex]\dfrac{x}{10}[/tex] 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 [tex]\dfrac{x}{15}[/tex] flowers in an hour.

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

[tex]6-1\dfrac{2}{3}=4\dfrac{1}{3}[/tex] hours.

Thus,

[tex]\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}.[/tex]