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!!!