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# re: help !

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re: help ! [#permalink]  10 Jul 2009, 13:32
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could some one tell me the formula for ansewring this question?

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
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Re: re: help ! [#permalink]  10 Jul 2009, 13:39
Expert's post
Moved to the appropriate Forum
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Re: re: help ! [#permalink]  10 Jul 2009, 14:08
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Quote:
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

Sally -a house in 4 hrs
1 hr -1/4

John -a house in 6 hrs
1 hr -1/6

Together sally and John in one hour complete
1/4+1/6 =6+4/24=10/24 =5/12

1 hr - 5/12 part of the house
? hr - whole house

Whole house = 12/5 =2 hrs 24 min
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Re: re: help ! [#permalink]  10 Jul 2009, 14:09
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Someone please correct me if I'm wrong. I'm a little rusty with rate/work problems.

Know this formula: R*T = W (Rate)*(Time) = Work

Sally: Rate * 4 hours = 1 house
Rate = 1/4

John: Rate * 6 hours = 1 house
Rate = 1/6

Working together, you combine their rates. So working together, their rate is: 1/4 + 1/6 = 10/24

So go back to the original equation R*T = W and make a new one with this new information. What do we know? Their rate is 10/24 houses/hour. They are going to paint 1 house (this is W). We need to find the time it takes (T). So we have:

(10/24)*T = 1
T = 24/10 = 12/5 hours

This is 2 and 2/5 hours. 2/5 of one hour is 24 min. So it will take 2 hours and 24 min. Answer A.

Also note that you can immediately eliminate answer choices D and E because Sally takes only 4 hours to paint a house. If John helps, no matter how slow/fast he paints, it will take less than 4 hours.
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Re: re: help ! [#permalink]  10 Jul 2009, 14:49
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wud just like to contribute a simpler method which i found very useful in doing faster calculations.

this method works for all "rate of doing work" problems, including distance and speed.

When rate of work is given, we usually have to calculate using reciprocals. instead take the lcm of all the rates of work of different people.
ie, here 4 hrs and 6 hrs,,,,,, lcm = 12

consider this lcm to be the total units of work to be done, ie, 12 units to be painted

Then, sally can paint the 12 units in 4 hours, or per hour she paints 3 units.
John paints 12 in 6 hours, so per hour he paints 12/6 = 2 units

Now both working together will paint 3+2 = 5 units per hour

To paint 5 units they take 1 hour, so to paint 12 units they will take 12/5 hours.

This method is excellent for doing simple calculations mentally. No need to use pen and paper. Try applying it to all time and work or speed and distance problems while practicing.
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Re: re: help ! [#permalink]  11 Jul 2009, 09:24
Nice one rashmine. Very sensible method.

I worked it out in normal way to get 12/5.

thanks
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Re: re: help ! [#permalink]  13 Jul 2009, 11:18
I worked it out the normal way as well and got confused by $$12/5 = 2.4$$ so 2 hours and 40% of 60 minutes.. Is there is way not to confuse when converting the decimals to hours and minutes ?
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Re: re: help ! [#permalink]  13 Jul 2009, 12:41
parimal wrote:
I worked it out the normal way as well and got confused by $$12/5 = 2.4$$ so 2 hours and 40% of 60 minutes.. Is there is way not to confuse when converting the decimals to hours and minutes ?

Donno if this helps, but I try to avoid using decimals when working with hr & minutes.

What I try to do is write the number as 2 2/5, however you still have to remember that 2/5 is of 60, not 100.
Re: re: help !   [#permalink] 13 Jul 2009, 12:41
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