Final answer:
Antonio and Wade, combining their efforts, can rake the lawn in 7.5 hours. This is calculated by adding their working rates (1/20 for Antonio, 1/12 for Wade) and taking the reciprocal of the sum (2/15).
Step-by-step explanation:
Antonio can rake the front lawn in 20 hours, meaning he can do 1/20 of the lawn in one hour. Wade can rake the lawn in 12 hours, meaning he can do 1/12 of the lawn in one hour. To find out how long it takes for them to rake the lawn working together, you need to add their rates of working.
Antonio's rate: 1/20 lawn per hour
Wade's rate: 1/12 lawn per hour
Working together:
1/20 + 1/12 = 3/60 + 5/60 = 8/60
8/60 simplifies to 2/15.
This means together they can complete 2/15 of the lawn in one hour. To find out how long it takes to complete one entire lawn, you take the reciprocal of their combined rate.
Time taken to rake the entire lawn together:
1 / (2/15) = 15/2 = 7.5 hours
So, working together, it will take Antonio and Wade 7.5 hours to rake the front lawn.