Question

Tammy can clean half of an area in an hour. Melissa can clean one-third of the area in an hour. How much of the area can they clean in 45 minutes?

Answer 1

Rate of Tammy (Time of Tammy) + Rate of Melissa (Time of Melissa) = Area Cleaned.

(Time of Tammy) = (Time of Melissa) = 45.

Rate of Tammy = \[\frac{ \frac{ 1 }{ 2 }area }{ 60 min }\]
Rate of Melissa = \[\frac{ \frac{ 1 }{ 3 }area }{ 60 min}\]

Answer 2

And then what?

Answer 3

So you plug things in and do the first equation I mentioned.

Answer 4

Remember to cancel things out too, including units. :)

Answer 5

I don't get it though. Usually, I'd be able to, but right now they just look like puzzle pieces that don't fit.

Answer 6

hmm. Okay. Lemme see if I can rephrase. :P

Answer 7

Thanks, that might help. :|

Answer 8

Okay, so Rate = how fast you can do something. How fast can Tammy clean half of an area?

Answer 9

In 30 minutes

Answer 10

So \[R = \frac{ area }{ time }\] In this case.

Answer 11

Thereby, in numbers, what is Tammy's Rate exactly?

Answer 12

Uhm, 30 minutes?

Answer 13

Ahh sorry my bad. Lemme say that again. Rate = \[\frac{ Area }{ Time }\]
Tammy cleans half an area in 1 hour. So divide that and you get the rate.

Answer 14

Rate of Tammy, at least.

Answer 15

1/120

Answer 16

1 in 2 hours or 120 minutes. Both correct. Let's switch it back to hours though, just for simpleness. So \[\frac{ 1area }{ 2hrs }\]

Answer 17

Do the same thing for Melissa. So \[\frac{ \frac{ 1 }{ 3 }area }{ 1hr }\]

Answer 18

20

Answer 19

Wait. 20 = \[\frac{ \frac{ 1 }{ 3 }area }{ 1 hr}?\]

Answer 20

No. I just found 1/3 of 60 though, which is 20.

Answer 21

:P Forget the minutes, again. Simply just do the division with hours.

Answer 22

Oh, :P
So it'd be 1 area in 3 hours?

Answer 23

Yep!

Answer 24

now 45 minutes is what fraction of an hour?

Answer 25

3/4

Answer 26

Now multiply both the rate of tammy and the rate of melissa with that, then add the two resultants and you have your answer.

Answer 27

So 1/2(3/4) + 1/3(3/4) = answer. Remember to cancel units out.

Answer 28

1/2(3/4) + 1/3(3/4) = 9/12 or 3/4

Answer 29

wait what? 1/2(3/4) = 3/8. whereas 1/3(3/4) = 3/12. Get the LCM of those and add.

Answer 30

Oh, I multiplied wrong. :P
Okay so it'd be 9/24 + 6/24 = 15/24
??? I feel like this makes less sense now.

Answer 31

Yep, now simply simplify that into 5/8 and you're right.

Answer 32

So memorize those equations and plug things in and you should be good on these questions for the rest of your life.

Answer 33

Oh, I didn't simplify. :P

Answer 34

Okay wait, so they cleaned 5/8 of the area in 45 minutes?

Answer 35

Yep. :P

Answer 36

Okay, now it makes sense, thanks for all your help. :)

Answer 37

No problem. :)