If John mows 40% of the lawn in 20 minutes, we can first find out how long it takes him to mow 100% of the lawn.
To find the time for 100%, we can use the following proportion:
\[ \text{Time for 40%} : \text{Time for 100%} = 40 : 100 \]
This means:
\[ \frac{20 \text{ minutes}}{x \text{ minutes}} = \frac{40}{100} \]
Cross-multiplying gives:
\[ 40x = 20 \times 100 \]
\[ 40x = 2000 \]
Now, divide both sides by 40:
\[ x = \frac{2000}{40} = 50 \text{ minutes} \]
Thus, it takes John 50 minutes to mow the entire lawn. Since he has already mowed 40% of the lawn in 20 minutes, he has 60% left.
To find out how much time is needed to mow the remaining 60%, we calculate:
\[ \text{Time for 60%} = 60% \text{ of total time} = 0.6 \times 50 \text{ minutes} = 30 \text{ minutes} \]
Therefore, John needs an additional 30 minutes to finish mowing the lawn.