Ian can rake a lawn and

bag the leaves in 5 hours. Kyandre can rake the same lawn

and bag the leaves in 3 hours. Working together,

how long would it take them to rake the

lawn and bag the leaves? So let’s think about

it a little bit. It says Ian can rake a lawn and

bag of the leaves in 5 hours. So for Ian, I for Ian. For 1 lawn, he can

do 1 lawn in 5 hours. We could have also written

this as 5 hours per lawn. But we’ll see that

writing it this way is more useful, because

it’s actually a rate. Because this is the same

thing as 1/5 lawns per hour. Or 1/5 of a lawn per hour. That’s the rate at

which Ian can rake a lawn, at 1/5 of

a lawn per hour. Now let’s do the same

thing for Kyandre. And this actually probably

shouldn’t be plural. 1/5 lawns, 1/5 of a lawn. So let me just

erase that S right there– 1/5 of a lawn per hour. Now let’s do the same

thing for Kyandre. Kyandre can rake the same lawn

and bag the leaves in 3 hours. So for Kyandre, Kyandre can,

for 1 lawn– I’ll assume it’s a boy’s name– he

can do it in 3 hours. Or if we were to

write it as a rate, this is 1/3 of a lawn per hour. Now let’s think about

what the combined rate is. So let’s say if we

have Ian plus Kyandre. What’s going to be

their combined rate? Well, they tell us that working

together, how long would it take them to rake

and bag the leaves? So let’s let let’s let t be

how long it will take them together. So that’s how long they

would take together. And if we say t is how

long they take together, then we could say

that combined, they will do 1 lawn in

every t hours, if we’re assuming t is in hours. For every t hours. Or as a rate,

their combined rate is going to be 1/t

of a lawn per hour. So that’s their combined rate. So here, we have the rate of

Ian and the rate of Kyandre, and the combined rate. So the combined

rate’s just going to be the sum of

each of their rates. If he can do 1/5

of a lawn per hour and he can do 1/3

of a lawn per hour, their combined rate is going

to be 1/5 of a lawn per hour plus 1/3 of an hour. Because in an hour he’ll

do 1/5, and he’ll do 1/3. So you’ll add those two

together to figure out how much they can do in an hour. So their combined rate is

going to be 1/5 lawn per hour. And I won’t write

the units here, just because it gets redundant. 1/5 lawn per hour I

could write over here. Plus 1/3 lawn per

hour for Kyandre. That’s going to be

their total rate, which is 1/t lawns per hour. And now we just

have to solve for t. And we’ll know the total number

of hours it will take them. So let’s do that. So to do that, we just

have to add 1/5 plus 1/3. Well, we have a common

denominator of 15. So this is the same

thing as 3/15 plus 5/15 is going to be equal to 1/t. And then we have a

common denominator now. So 3 plus 5 is 8. So this is going to be 8/15. I’ll go over here now. So now we have 3 plus 5 is 8. Over 15 is equal to 1 over t. If we want to solve

for t, we could take the reciprocal

of both sides. So if we flip the left

side, we get 15/8. And if we flip the right

side, we get t/1, or just t. So it’ll take them 15/8 hours. Or if we want that

in kind of a way that we can think about it a

little bit better, 15/8– so t is equal to 15 over 8 hours. And I should say 15

over 8 hours per lawn. This whole time here

we had lawns per hour. This was lawn per hour. And this was here as

well, lawns per hour. When we flip it, it

becomes hours per lawn. So that’s exactly what we want. But 15/8 is the same

thing as 1 and 7/8 hours. And 7/8 of an hour– we

can get our calculator out. If we have 60 minutes

in an hour, times 7/8, we get 52.5 minutes. So this is equal to our answer. Combined, it will take them 1

hour and 52.5 minutes per lawn. Or to do this lawn right over

here, the lawn in question. Hopefully, you

found that useful.

One teeth of a lawn… per hour…..

Lawns are dangerous savages….

Rakin' the Lawn, and Bagin' the leaves.

your videos are helping me out so much in preparing for my ASVAB. 4 yrs after graduation i forgot alot of math thanks 👍

Thank you! Helped me more than my professor that loves to only teach verbally.

GOD BLESS UUUUUUUUUUUUUUUUU thank you

your videos are amazing! I just found it a bit funny that you assumed kyandre was a man because he could rake the leaves faster, even though it could easily be a woman's name. just a bit of perspective. Thanks for the videos