math help!

[Ksandra]

Ok, so on Saturday I take a test called the CBEST in order to substitute teach in California. It has a reading, writing, and math section (have to pass all parts). I've been studying since I signed up a month ago (that's when I heard about it), and this/last week been spamming practice tests to try and get ready. Really nervous and I am still kinda shaky on the math stuff (I was an English major what can I say?)

Anyways, long story short, I got this question from a site. Unfortunately, even though the site gives the answer it doesn't explain how to get it. I can't seem to figure out how you find the solution. Please help me out with a formula for it!


Please don't give like a "well this doesn't make sense, so has to be this" kind of answer. I need the formula for it since a similar question could be on the test, but may not have an easy elimination process with their choices.

Ok here's the question

2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes



spoiler below has the answer if you think it'll help you with remembering how you solve something like this.

[spoiler:301n99l0]Answer is A.[/spoiler:301n99l0]

[Jotaru]

The way I did it that makes sense to me... not sure if its a legit 'formula' like you need, but I've always felt like I'm pretty decent at math yet do these types of problems my own way...

Sally = 1 house / 4 hours
John = 1 house / 6 hours (their respective rates)

Combine them, they are working together.

1/4 = 6/24
1/6 = 4/24

Combined = 10/24 = 1house/2.4 hours
2.4 x 60(minutes) = 144 minutes or 2 hours, 24 minutes

[Tythera]

Sally paints the house in 4 hours, meaning 1/4 of the house per hour
John paints the house in 6 hours, meaning 1/6 the house per hour

1 hour passes (3/12 + 2/12, 5/12 the house has been painted)
2 hours pass (5/12 + 5/12, 10/12 the house has been painted)

They have 2/12 the house remaining to paint, and they can do 5/12 in an hour, so it takes 2/5 of an hour which is 24 minutes.

Edit: wow, the posts happened so close I didn't even get the warning and when it first took me to my post it was just mine and the OP

[Odon]

Answer F: Hire day workers to paint the house!

[archibaldcrane]

In one minute, Sally can paint 1/240th (60 minutes times 4 hours) of a house.
In one minute, John can paint 1/360th of a house.

Combined, they can paint 1/240+1/360 of a house, or 3/720+2/720=5/720 of a house in a minute.

720 divided by 5 = 144 minutes combined to paint a house, so 2 hours 24 mins.

[shihei]

educated guessing gets rid of 3 (if not all but the correct one) answers easily unless Sally and John are sexing it up.

archi's math looks the easiest to understand.

[Delenn]

Off the top of my head, the simplest explanation is to:
1) Figure out how fast each of them can paint houses (houses per hour)
2) Figure out how fast both of them can paint houses together (add)
3) Figure out how long it'd take to paint one house (solve the proportion)

-----

1) From the problem statement, you know that Sally can paint 1/4 houses per hour and that John can paint 1/6 houses per hour

2) 1/4 + 1/6 = 3/12 + 2/12 = 5/12 houses per hour together

3) Now you can use a proportion:

5 houses   1 house
-------- = -------
12 hours   x hours

Cross multiply to solve for x.

5*x = 12*1
x = 12*1/5
x = 12/5

12/5 hours = 2 + 2/5 hours = 2 hours + 24 minutes

Hope that helps,

[aurik]

In before mythical-man-month.

[Ksandra]

omg thank you guys!!!! ><; lmao actually reading the different ways made it more sense to me (like reconfirming it)

Let's just hope I remember this -.-;