Four people can mow a lawn in 6 hours. How many more people will be needed to mow the lawn in 4 hours, assuming each person mows at the same rate?
I want to compare the rate of mowing for different numbers of people and different times. Let me define a variable r to be the rate of mowing for one person in lawns per hour. Then, if four people can mow a lawn in 6 hours, I can write an equation: 4r * 6 = 1, where 1 is the number of lawns mowed. Solving for r, I get r = 1/24, so one person can mow 1/24 of a lawn in one hour. Now, let me see how many people are needed to mow the lawn in 4 hours.
[* [ I can write another equation: nr * 4 = 1, where n is the number of people. Substituting r = 1/24, I get n * 1/24 * 4 = 1, which simplifies to n = 6. This means I need 6 people to mow the lawn in 4 hours. Therefore, I need 6 - 4 = 2 more people than before. 