Let's solve the problem step by step.
1. Understanding the given information:
- John mows 40% of the lawn in 20 minutes.
2. Finding the total time required to mow the lawn:
- We know that 40% of the lawn takes 20 minutes.
- To find the total time needed to mow the entire lawn (100%), we set up the proportion:
[tex]\[ \frac{40\%}{100\%} = \frac{20 \text{ minutes}}{x \text{ minutes}} \][/tex]
- Solving for [tex]\( x \)[/tex], the total time needed to mow the lawn, we can cross-multiply:
[tex]\[ 40\% \times x = 100\% \times 20 \text{ minutes} \][/tex]
[tex]\[ 40x = 2000 \][/tex]
[tex]\[ x = \frac{2000}{40} \][/tex]
[tex]\[ x = 50 \text{ minutes} \][/tex]
Therefore, the total time required to mow the lawn is 50 minutes.
3. Calculating the additional time needed to finish mowing:
- John has already spent 20 minutes mowing 40% of the lawn.
- The additional time needed to finish mowing the remaining 60% is:
[tex]\[ \text{Total time} - \text{Time already spent} \][/tex]
[tex]\[ 50 \text{ minutes} - 20 \text{ minutes} = 30 \text{ minutes} \][/tex]
Therefore:
- The total time needed to mow the lawn is 50 minutes.
- It will take John 30 more minutes to finish mowing the lawn.
So, the equivalent fractions are:
[tex]\[ \frac{40\%}{100\%} = \frac{20 \text{ minutes}}{50 \text{ minutes}} \][/tex]
To summarize:
- The total time needed to mow the lawn is 50 minutes.
- It will take John 30 more minutes to finish mowing the lawn.
