Math inclined..?

Question

I have been studying really hard for my SAT, which takes place tomorrow. however, I've got things down pretty well you know? but I'm always stuck on the same type of question:

"if sammie can paint a fence in 4 hours, and george can paint it in 6, how fast can they get it done together?"

"If it takes cindy 30 minutes to fill a pool with buckets of water, john takes 45 minutes, and jack takes 1 hour and 30 minutes, how fast could they do it together?"

I've tried really hard i promise... but I always* get these questions wrong... I've checked several websites about it too :( please, could anyone tell me how to do either one of these? (without refering me to a website)?

thank you so much :)

Answer 1

These are generally done by setting up fractions. For Sammie and George, the equation would be x/4 + x/6 = 1. The 1 signifies the whole job being completed. The x's mean that both people will work the same amount of time together.

Multiply by 12 to get rid of the fractions.
3x + 2x = 12
5x = 12
x = 2 2/5 hours.

For Cindy, John and Jack, change their times to minutes and do the same thing.
x/30 + x/45 + x/90 = 1
Multiply by 90 to get rid of the fractions.

3x +2x + x = 90
6x = 90
x = 15 minutes

Good luck on your test.

Answer 2

sammie's rate is 4hrs/fence and george's rate is 6hrs/fence
there's one fence so the time is constant

so 1 fence per time t
t(1/4+1/6)=1
12=5t
t=12/5 hrs

for cindy and john and jack, convert the times to hours
and use the same approach
t(2+ 4/3 *2/3)=1
12t=3
t=1/4

15minutes

j

Answer 3

I think you just take the average of the times. Like for the first one, I think it would be 5. You could probably check that answer on the Internet, so you can see if I'm right or not.

I'd probably get confused on these things too, so don't feel bad. And good luck on ur SAT!

Answer 4

x = first time
y = second time

xy/(x+y) = time for both together

check: make sure your answer is less than the fastest worker

24/10 = 2.4 hrs

more than 2 is a little tricker but uses the same concept.

xyz/(x+y+z)

.5 * .75 *1.5 / (.5+.75+1.5)
= 0.204545 hrs = 12.27 min

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suppose they work the same fast ....
4 hrs to paint the fence
2 workers = 4/2 = 2 hours (that's the quickest time so your answer for different work rates must be higher)

30 min to fill pool
3 workers = 30 / 3 = 10 minutes (absolute fastest time)

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so you know your first answer must be between 2 hrs and less than 4 hrs

likewise your second answer must be between 10 min and 30 min.

Answer 5

there are 60 min in an hour so you 60 times 4 . then 60 times 6 and add

Answer 6

I believe the answer to your first question is 5 hours

And the answer to your second question is 55 minutes