Complete the following word problems.
14.It takes 9 hours for Isabella to rake leaves by herself,but her brother Matthew can work three times as fast.If they work together, how long will it take them to rake leaves?
Rate Time Work Done
Isabella
Matthew
I think the answer is 3 hours
Isabelle's rate = lawn/9
(Matt could do it in 3 hours)
Matt's rate = lawn/3
combined rate = lawn/9 + lawn/3 = 4lawn/9
time at combined rate = lawn/(4lawn/9))
= 9/4 hrs or 2.25 hrs or 2 hours and 15 minutes
( since "lawn" canceled, we could have just used
1/9 + 1/3 = 4/9
then time = 1/(4/9) = 9/4 = 2.25 )
To solve this problem, we need to first find the rate at which Isabella works and the rate at which Matthew works. Then we can combine their rates to find the time it would take for them to complete the work together.
Given information:
Isabella takes 9 hours to rake leaves by herself.
Matthew can work three times as fast as Isabella.
Let's start by finding their rates:
Isabella's rate: In one hour, Isabella can complete 1/9th of the work. (Since she takes 9 hours to complete the work)
Matthew's rate: Matthew can work three times as fast as Isabella. Therefore, his rate is 3/9, which simplifies to 1/3. (Three times the rate of Isabella)
Now, to find their combined rate when working together, we can add their rates:
Combined rate = Isabella's rate + Matthew's rate
Combined rate = 1/9 + 1/3
Combined rate = 4/9
This means that together, Isabella and Matthew can complete 4/9th of the work in one hour.
To find how long it would take them to complete the entire work, we need to divide the total work by their combined rate:
Time to complete the work = Total work / Combined rate
Time to complete the work = 1 / (4/9)
Time to complete the work = 9/4
Therefore, if Isabella and Matthew work together, it will take them 9/4 or 2.25 hours to rake the leaves.