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

Answer: There are 1500 flowers altogether.

Step-by-step explanation:

Since we have given that

Time taken by Group A to complete the task = 10 hours

Time taken by Group B to complete the task = 15 hours

But Group B took a break for 1 hour and 40 minutes, and Group B ended up making 300 more flowers than Group B. Group A done extra work for 1 hour 40 minutes. i.e.

$1\frac{40}{60}\\\\1\frac{4}{6}\\\\=1\frac{2}{3}\\\\=\frac{5}{3}\\\\\text{Group A  has done}=\frac{5}{3}\times \frac{1}{10}=\frac{1}{6}$

Let the total number of flowers altogether they made be 'x'.

According to question,

$(\frac{x}{10}+\frac{x}{6})-\frac{x}{15}=300\\\\\frac{3x+5x-2x}{30}=300\\\\\frac{6x}{30}=300\\\\\frac{x}{5}=300\\\\x=300\times 5=1500$

Hence, there are 1500 flowers altogether.