Question

Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a chimney in 1 5/7 hours. If it takes Kalon 4 hours to clean a 20-foot chimney by himself, how long does it take Marna to clean the same size chimney by herself?

Answer 1

\[\frac{ kalon }{ h } = chimney\]\[\frac{ Marna}{ h } = chimney\]the hours they need are not the same, right?

Answer 2

no i don't think so.

Answer 3

we can write how fast they are in terms of 1 chimney.
\[Kalon:\frac{ chimney }{ 4h }\]\[Marna:\frac{ chimney }{ ?h }\]

Answer 4

if we want to add them together (Working together)
we must get a common denominator.

you will see this in the formula that is used for problems like this

Answer 5

\[Kalon:\frac{ chimney \times ?h }{ 4h \times ?h}\]\[Marna:\frac{ chimney \times 4h}{ ?h \times 4h}\]

Answer 6

do you have some idea where we get this from so far? :)

Answer 7

yeah

Answer 8

great

Answer 9

kalon: 1/4 ( 1 chimney per 4 hours)
marna: 1/x <- we don't know how long it takes for marna to make a chimney yet

1/4 + 1/x = the amount of chimneys they do together

Answer 10

verify if this is correct

Answer 11

The working together formula is

\(\dfrac{K \times M}{K + M} = t\)

K = amount of hours Kalon can clean the chimney alone
M = amount of time Marna can clean the chimney alone.
t = the time both can clean the chimney together.

Answer 12

thanks Hero :)

Answer 13

I knew there was this equation, I couldn't remember it from my mind

Answer 14

In this case,

\(t = 1 + \frac{5}{7}\) in hours
\(M = 4\) in hours

We need to find K

Answer 15

For convenience, we can express \(t\) as \(\dfrac{12}{7}\)

Answer 16

@AlexaLeyva I hope you can see better why the formula Hero uses works :) it is related to the work we have done

Answer 17

yeah it is. thanks anyways @mathessentials

Answer 18

thank you @Hero

Answer 19

So to set up the equation we have:

\(\dfrac{4K}{4 + K} = \dfrac{12}{7}\)

\(28K = 12(4 + K)\)

\(28K = 48 + 12K\)

\(28K - 12K = 48\)

\((28 - 12)K = 48\)

\(16K = 48\)

\(K = \dfrac{48}{16}\)

\(K = 3\)

So Karna can clean the chimney alone in 3 hours

Answer 20

thats what i got