Question

Selmas class making a care package to give to victims of a natural disaster.Selma packs one box in 5 minutes and has already packed 12 boxes. Her friend Trudy packs one box in 7 minutes and has already packed 18 boxes. How many more minutes does each to work in order to have packed the same number of boxes?

Answer 1

Each of them need to work 105 minutes more in order to have packed the same number of boxes.

Explanation

Suppose, they need to work for $x$ minutes more in order to have packed the same number of boxes.

Selma packs one box in 5 minutes and Trudy packs one box in 7 minutes.

So, the number of boxes packed by Selma in that $x$ minutes $=\frac{x}{5}$ and the number of boxes packed by Trudy in $x$ minutes $=\frac{x}{7}$

Given that, Selma and Trudy have already packed 12 and 18 boxes.

Now if each of them packed the same number of boxes, then the equation will be......

$12+\frac{x}{5}=18+\frac{x}{7}\\ \\ \frac{x}{5}-\frac{x}{7}= 18-12\\ \\ \frac{7x-5x}{35}=6\\ \\ \frac{2x}{35}=6\\ \\ 2x= 210\\ \\ x= \frac{210}{2}=105$

So, each of them need to work 105 minutes more in order to have packed the same number of boxes.