Question

If Dominik completes a project by himself, it will take him 8 hours. Working with Katarina, it will take them 5 hours. If they work together, what is the missing value from the table that represents the part of the project Dominik will complete? 8r 8(5) r (5)

Answer 1

The main formula we use here is Work=Rate*Time,


1. The rate (speed of working) of Dominik is 

$r_D=1project/8hours= \frac{1}{8}(prj/h)$

2. Let the the rate of Katarina be $r_K=x(prj/h)$

Together they have a rate of $r_D_K$ equal to $\frac{1}{8}+x$ (project per hour)

so $(\frac{1}{8}+x) ( \frac{proj}{hr})*5(hr)=1(proj)$

simplify the units:

$(\frac{1}{8}+x) *5=1$

$\frac{1}{8}+x = \frac{1}{5}$

$x= \frac{1}{5}- \frac{1}{8}= \frac{8-5}{40}= \frac{3}{40}$

so the rate of Katarina is 3/40 (proj per hour)

Now, the rate of Dominik was 1/8 (pr/hr)=5/40 (pr/hr)

In 5 hours Dominik complets 5*5/40=25/40 of the project

Katarina completes 5*3/40=15/40 of the project.

Answer 2

Answer:

The part of the project Dominik will complete when they work together

= (5/8) of the entire work.

Step-by-step explanation:

Let Dominik's speed = d

Let Katarina's speed = k

Let the amount of total work to be done be x

Speed = (Amount of work/time)

For Dominik

d = (x/8)

x = 8d (eqn 1)

when they work together.

Speed = (x/5)

Work done by Dominik in the 5 hours = 5d

Work done by Katarina in the 5 hours = 5k

Total work done = x = (5d + 5k)

Recall eqn 1, x = 8d

8d = 5d + 5k

3d = 5k

k = (3d/5) (eqn 2)

So, back to when Dominik and Katarina work together.

Total work done by Dominik = 5d

Total work done by Katarina = 5k = 5(3d/5) = 3d

So, the part of the project Dominik will complete when they work together

= 5d ÷ (5d + 3d) = 5d ÷ 8d = (5/8)

Bonus

Katarina completes 3d ÷ (3d + 5d) = 3d ÷ 8d = (3/8) of the total work when they work together.

Hope this Helps!!!