Kyle and Andrew decide to make some money by raking leaves in their neighborhood. The houses in their neighborhood each have half acre lawns. Kyle and Andrew each start by raking the leaves from their own yards. Kyle realizes it takes him 3 hours to rake one yard and Andrew takes 4 hours. Working together on Saturday, they spend 8 hours total raking yards around their neighborhood. How many yards did they rake? Express your answer as a mixed number.



Kyle and Andrew continue raking leaves again on Sunday and Monday after school. They rake the yard of every house in their neighborhood. There are 14 houses in their neighborhood. If they charge $6 per hour of work, how much money will Kyle and Andrew make after they are finished raking all of the leaves in the neighborhood?



Since Kyle raked at a faster rate than Andrew, Andrew suggests they split their earnings proportional to how much of the 14 yards they each raked. How much more money did Kyle earn than Andrew on their yard work?

In one hour Kyle can do 1/3 yard

In one hour Andres can do 1/4 yard

so in 8 hours they can do 8(1/3) + 8(1/4)
= 8(1/3 + 1/4) yards
= 8( 7/12) yards
= 14/3 yards or 4 2/3 yards

They can do 14/3 yards (houses) in 8 hours
then they can do 14 yards in x hours

(14/3) / 14 = 8/x
(14/3)x = 112
x = 112(3/14) = 24

it would take 24 hrs to do the 14 yards, at $6 per hour , that would be $144

Now, your turn.
What would be the ratio of the work done by the two boys?
Split your $144 into that ratio.

Didn’t it say it takes them 3 hours to do one yard and the other 4 hours? So if they did 14 yards wouldn’t it take 49 hours

To find the number of yards they raked on Saturday, we need to determine the combined rate at which Kyle and Andrew can rake yards.

First, let's find out how long it takes them to rake one yard together. We can do this by calculating the sum of their individual rates.

Kyle takes 3 hours to rake one yard, so his rate is 1 yard / 3 hours, or 1/3 yard per hour.
Andrew takes 4 hours to rake one yard, so his rate is 1 yard / 4 hours, or 1/4 yard per hour.

To find their combined rate, we add their individual rates: 1/3 + 1/4 = 7/12 yard per hour.

Since they worked together for a total of 8 hours on Saturday, the total number of yards they raked can be found by multiplying their combined rate by the number of hours they worked.

Total yards = (7/12) yard per hour * 8 hours = 7/12 * 8 = 14/3 yards.

So, they raked a total of 14/3 yards on Saturday.

For the second part of the question, let's calculate how much money Kyle and Andrew will make after raking all the leaves in the neighborhood.

They charge $6 per hour of work, and they worked a total of 8 hours on Saturday, as well as additional hours on Sunday and Monday after school. Let's assume they worked the same number of hours on each of these days.

Total hours worked = 8 hours on Saturday + 3 days * x hours each day (where x is the number of hours worked per day).

The total number of hours worked must be equal to the number of houses in the neighborhood times the hours it takes to rake one yard.

Since there are 14 houses in the neighborhood and it takes Kyle 3 hours to rake one yard, the equation becomes:

8 hours on Saturday + 3 days * x hours each day = 14 houses * 3 hours per yard.

Simplifying the equation, we get:

8 + 3x = 14 * 3,
8 + 3x = 42,
3x = 42 - 8,
3x = 34,
x = 34 / 3.

So, each day they worked 34/3 hours.

The total number of hours they worked can be found by summing the hours from each day:

Total hours worked = 8 hours on Saturday + 3 * (34/3) hours = 8 + 34 = 42 hours.

Finally, we can calculate their earnings by multiplying the total number of hours worked by the rate of $6 per hour:

Total earnings = 42 hours * $6 per hour = $252.

Therefore, Kyle and Andrew will make $252 after raking all the leaves in the neighborhood.

For the last part of the question, let's calculate how much more money Kyle earned than Andrew on their yard work.

Since they decided to split their earnings proportionally to the number of yards they each raked, we need to find the proportion of yards each of them raked.

Kyle raked his own yard on Saturday, which we determined to be 1 yard. Therefore, he raked 1/14 of the total yards in the neighborhood.

Andrew also raked his own yard on Saturday, so he raked 1/14 of the total yards as well.

Since there are 14 houses in the neighborhood, they raked a total of 14/14 = 1 yard each.

Therefore, Kyle and Andrew raked an equal number of yards, and Kyle did not earn more money than Andrew in this scenario.