Question

1. Working alone, Emma can dig a 13 ft by 6 ft hole in 8.5hours. Kennedy can dig the same hole in 14 hours. How longwould it take them if they worked together?

Answer 1

We know that

• Emma can dig a 13 ft by 6 ft hole in 8.5 hours.

,

• Kennedy can dig the same hole in 14 hours.

We are going to express the "hole" as unit 1 since both of them did one. The following rates express the job done for each person.

• Emma rate = 1/8.5 (job per hour)

,

• Kennedy rate = 1/14 (job per hour).

,

• The rate where they work together is 1/x.

Now, we form the equation with those rates

`(1)/(x)=(1)/(8.5)+(1)/(14)`

Then, we solve for x, we sum the fractions first

`\begin{gathered} (1)/(x)=(14+8.5)/(119) \\ (1)/(x)=(22.5)/(119) \end{gathered}`

Now, we multiply in cross form

`\begin{gathered} 1\cdot119=22.5\cdot x \\ 22.5x=119 \end{gathered}`

Then, we divide the equation by 22.5

`\begin{gathered} (22.5x)/(22.5)=(119)/(22.5) \\ x\approx5.29 \end{gathered}`

Therefore, if they work together, they will finish the hole in 5 hours approximately.