Final answer:
Katie completes mowing the entire lawn faster than Ken. Ken would take 48 minutes, while Katie would take only 33.33 minutes to mow the 10,000 square feet lawn completely.
Step-by-step explanation:
The question asks us to determine who would complete mowing an entire 10,000 square feet lawn faster between Ken and Katie. To find this, we will compare their rates of mowing.
Ken can mow 1/4 of the lawn in 1/5 of an hour. This means he would take 4 times 1/5 of an hour to mow the entire lawn, which is 4/5 of an hour or 48 minutes. On the other hand, Katie can mow 3/5 of the lawn in 2/6 of an hour (or 1/3 of an hour, which is 20 minutes). To find out how long it takes for Katie to mow the entire lawn, we can set up a proportion where 3/5 corresponds to 20 minutes, thus 1 corresponds to (20 minutes ÷ 3/5) which is 33.33 minutes (or exactly 100/3 minutes).
Comparing their times, we see that Katie can mow the entire lawn in 33.33 minutes, which is less time than Ken's 48 minutes. Hence, Katie completes mowing the entire lawn faster than Ken.