Question

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?

Answer 1

`(6750)/(7)`

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
`(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
`(x)/(15)` flowers in an hour.

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

`6-1(2)/(3)=4(1)/(3)` hours.

Thus,

`(x)/(10)\cdot 6-(x)/(15)\cdot 4(1)/(3)=300,\\ \\(3x)/(5)-(13x)/(45)=300,\\ \\14x=300\cdot 45=13500,\\ \\x=(13500)/(14)=(6750)/(7).`