Question

Working alone, it would take shandra 45 minutes to mow the lawn. to mow the same lawn, also working alone, it would take kelly 1 hour and 15 minutes. if they work together, the girls believe it will take them 1 hour to mow the lawn. which best describes the reasonableness of their solution? their estimate is longer than the time it will actually take: their estimate is accurate: their estimate is shorter than the amount of time it will actually take: their estimate is longer than the time it will actually take:

Answer 1

To solve this work problem, we are going to use the work formula:
`(t)/(a) +(t)/(b) =1`

where

`t` is the time it takes to complete the work working together.

`a` is the time it takes the first person to complete the work.

`b` is the time it takes the second person to complete the work.

We know from our problem that it takes Shandra 45 minutes to mow the lawn (complete the work), so
`a=45`.

We also know that it takes Kelly 1 hour and 15 minutes to complete the work. Notice that the Shandra's time is in minutes, while Kelly's time is in hours and minutes. Since we need to express the time in the same units, we are going to convert Kelly's time to minutes only. We know that there are 60 minutes in one our, so 1 hour and 15 minutes is 60 minutes + 15 minutes = 75 minutes. Now we know that Kelly's time to complete the work is 75 minutes, so
`b=75`. Let's replace the values in our formula and solve for
`t`:

`(t)/(a) +(t)/(b) =1`

`(t)/(45) +(t)/(75) =1`

`5t+3t=225`

`8t=225`

`t=(225)/(8)`

`t=28.125`

Now we show that it will take the girls 28.125 minutes (almost half and hour) to mow the lawn working together. We can conclude that their estimate is longer than the time it will actually take.