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
Abbe's rate = 1/15 lawns/min
Ben's rate = 1/20 lawns/min
Carls' rate = 1/30 min
combined rate = 1/15 + 1/20 + 1/ 30 = 3/20 lawn/min
but they mowed for 5 minutes
so time x rate = 5(3/20) = 15/20 or 3/4
They mowed 3/4 of the lawn
To find out what part of the lawn was mowed, we need to calculate the combined mowing rate of Abe, Ben, and Carl.
First, let's find the mowing rate of each person:
- Abe's mowing rate: 1 lawn / 15 minutes = 1/15 lawns per minute
- Ben's mowing rate: 1 lawn / 20 minutes = 1/20 lawns per minute
- Carl's mowing rate: 1 lawn / 30 minutes = 1/30 lawns per minute
Now, let's combine their mowing rates to find the total mowing rate when they work together. Since they work together for 5 minutes, we can multiply their individual rates by 5:
- Abe's rate when working together: (1/15 lawns per minute) * 5 minutes = 1/3 of a lawn
- Ben's rate when working together: (1/20 lawns per minute) * 5 minutes = 1/4 of a lawn
- Carl's rate when working together: (1/30 lawns per minute) * 5 minutes = 1/6 of a lawn
Now we can add up their individual mowing amounts to find the total mowed:
- Total mowed = Abe's amount + Ben's amount + Carl's amount
- Total mowed = 1/3 + 1/4 + 1/6
- Total mowed = (8/24) + (6/24) + (4/24)
- Total mowed = 18/24
- Simplifying the fraction, we get: Total mowed = 3/4
Therefore, the answer is option c. 3/4 of the lawn was mowed.