Kiana takes 2 hours to wash 500 dishes, and daisha takes 3 hours to watch 450 dishes. how long will they take, working together, to wash 1000 dishes?

In this problem, imagine you're Kiana & Daisha. You have a goal of washing 1000 dishes together; not when one of you finish. You need to figure out how much time would it take to wash the dishes.

Shorter Way
We could do this by multiplying 500 and some number until we get 1000 dishes. 

  500   x     ?      =       1000
dishes |  hours |   goal of dishes
for 2 hrs

We could do this by 1000 dividing by 500 which is 2 multiplied by 2 which is 4 hours to complete this task for one person.

Proper Way
Now, do the same thing with a proper way. Find the unit rate which is 450 divide by 3 which is 150 and take that into the model.

  150   x     ?      =       1000
dishes |  hours |   goal of dishes
for 1 
hour

Divide 1000 by 150 and it will take 6.6666... but that's not reasonable. So, it would take more than 6 hours so let's just put 7 hours. Add 7 hours and 2 hours which is 9 hours.