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

Answer: D. 1/8 (5)

Explanation:

Answer 2

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


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


`r_D=1project/8hours= (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
`(1)/(8)+x` (project per hour)

so
`((1)/(8)+x) ( (proj)/(hr))*5(hr)=1(proj)`

simplify the units:


`((1)/(8)+x) *5=1`


`(1)/(8)+x = (1)/(5)`


`x= (1)/(5)- (1)/(8)= (8-5)/(40)= (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.