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: mc027-1.jpg Their estimate is accurate: mc027-2.jpg Their estimate is shorter than the amount of time it will actually take: mc027-3.jpg Their estimate is longer than the time it will actually take: mc027-4.jpg

Answer 1

You can estimate the time that it will take both to mow the lawn working together by adding up the individual velocities.

The velocity of Sandra is 1 lawn / 45 minutes.

The velocity of Kelly is 1 lawn / 1 hour and 15 minures = 1 lawn / 75 minutes

The velocity together is 1 lawn / 45 minutes + 1 lawn / 75 minutes.

That sum of the fractions is:


`(1)/(45) + (1)/(75) = (75+45)/(45*75) = (120)/(3375) = (8)/(225)`

That is velocity = 8 lawns / 225 minutes.

So, the time to mow one lawn is: t = 1lawn / velocity =
`(1)/( (8)/(225) ) = (225)/(8) = 28.125 minutes`

So, the time is about 28 minutes, which means that their estimate is longer than the time it will actually take.