Question

Sarah can paint a small room in 45 minutes. Sam can paint that same room in 20 minutes. If they work together, how long will it take them to paint the room?

Answer 1

Im not asking for someone to do it for me but to help me out the whole way through. :)

Answer 2

If Sarah works for 1 minute she can paint 1/45 of the room.
If Sam works for 1 minute he can paint 1/20 of the room.
Can you see what fraction of the room will be painted if they work together for 1 minute?

Answer 3

Thank you :) im going to review my notes really quick and try and set it up may I tag you in it once im ready? :)

Answer 4

Please do :)

Answer 5

So I rewatched a live lesson and I have to use the Fraction Buster Method. Do you know what that is?

Answer 6

If they work together for one minute the fraction of the room that will be painted is found as follows:
\[\large \frac{1}{45}+\frac{1}{20}=\frac{4+9}{180}=\frac{13}{180}\]

Answer 7

whered the 4 and 9 come from?

Answer 8

The addition of the two fractions 1/45 and 1/20 was performed by first finding the Lowest Common Multiple of 45 and 20, which is 180. Then both fractions are converted to 180ths and added.
1/45 = 4/180 and 1/20 = 9/180

Answer 9

is that the answer? or when its simplified is that the answer?

Answer 10

I got 20

Answer 11

When both are working together for 1 minute they paint 13/180 of the room. Let t be the number of minutes needed for both working together to complete painting the room. Then we can write:
\[\large t \times \frac{13}{180}=1\ .............(1)\]
Now just solve equation (1) to find the value of t which is the time required in the question.

Answer 12

Okay hold on a sec :)

Answer 13

\[45\times\frac{ 13 }{ 180}=\frac{ 13 }{ 4 }\]

Answer 14

\[20\times \frac{ 13 }{ 180}=\frac{ 13 }{ 9 }

Answer 15

well for the last one I got 13 over 9

Answer 16

\[\large t \times \frac{13}{180}=1\]
Multiplying both sides by 180/13 we get:
\[\large t=\frac{180}{13}=(you\ can\ calculate)\ minutes\]

Answer 17

Im very confused...

Answer 18

Which step don't you understand?

Answer 19

So what I calculated was wrong , right?

Answer 20

You don't seem to be doing what I asked.

Answer 21

And what is it you asked?

Answer 22

When I asked you to solve:
\[\large t \times \frac{13}{180}=1\ .............(1)\]
you substituted 45 for t. That is not correct.

Answer 23

To solve (1) just multiply both sides by 180/13 to get:
\[\large t=\frac{180}{13}\]

Answer 24

OKay then.. what do I do for that step?

Answer 25

Just divide 180 by 13 to get the time it would take to paint the room with Sarah and Sam working together.

Answer 26

Thank you !

Answer 27

You're welcome :)