Abe can mow the lawn in 15 minutes. Ben can mow the lawn in 20 minutes.Carl can mow the lawn in 30 minutes.They work together for 5 minutes.What part of the lawn was mowed?
a. 1/4
b. 2/3
c. 3/4
d. 4/5
e. all of it
please answer and explain
since 1/15 + 1/20 + 1/30 = 3/20, they can do the job together in 20/3 minutes.
5/(20/3) = 3/4
To determine what part of the lawn was mowed, we need to calculate the total time it takes for all three of them working together.
First, we calculate the rate at which each person mows the lawn:
- Abe mows the lawn in 15 minutes, so his mowing rate is 1/15 of the lawn per minute.
- Ben mows the lawn in 20 minutes, so his mowing rate is 1/20 of the lawn per minute.
- Carl mows the lawn in 30 minutes, so his mowing rate is 1/30 of the lawn per minute.
To find the total mowing rate when they work together, we add up their individual rates:
1/15 + 1/20 + 1/30 = (4/60) + (3/60) + (2/60) = 9/60 = 3/20 of the lawn per minute.
Now, we need to calculate the portion of the lawn that was mowed in 5 minutes when they worked together. To do this, we multiply the mowing rate by the time:
(3/20) * 5 = 15/20 = 3/4 of the lawn.
Therefore, the correct answer is (c) 3/4 of the lawn was mowed.