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goldie45Posted - 2 October 2006 0:21  Show Profile
How do you solve this question? The answer is 2 hours and 24 minutes, but I'm not sure how they came up with it.

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?

zuzuspedals Posted - 8 October 2006 12:35  Show Profile
Can anyone explain this answer? I too would like to see how it is worked. Thank you.
Georgene Posted - 12 October 2006 19:20  Show Profile
I think that I have it figured out.</P><P>Set this problem up as a fraction that you will add, then you will divide the smaller number into the larger number (time).</P><P><BR>Number of people 1 1<BR>_____________= ___ + __<BR>time 4 6</P><P></P><P>Find the commom denominator (12) and add the fractions.</P><P>3 2 5<BR>__ + ___ = ___<BR>12 12 12</P><P></P><P>Now solve for 12 hours divided by 5 and you will get an answer of 2 hours and 2/5 of an hour. 2/5 of an hour equals 24 minutes. So, your answer is 2 hours 24 minutes.</P><P>I solved for 2/5 of an hour by setting it up as a proportion.</P><P>2 ?<BR>__ = ___<BR>5 60</P><P>Cross multiply 2 x 60 (equals 120), and divide by 5. 120 divided by 5 = 24.
Georgene Posted - 12 October 2006 19:21  Show Profile
Sorry, that did not show right. But I hope you have the idea on how I solved it.
goldie45 Posted - 17 October 2006 0:32  Show Profile
I'm still a little confused
Georgene Posted - 17 October 2006 16:33  Show Profile
Sally is painting 1/4 of the time and John is painting 1/6 of the time. To solve this problem, you add the two fractions together. First, you must find a common denominator.. which could be 12. Using the common denominatior you add 3/12 + 2/12 which equals 5/12.</P><P>Total time is 1, and the part used is 5/12. To solve take 1 divided by 5/12. When you divide fractions, take the second fraction and invert it and multiply the fractions, thus you have 1 times 12/5... which equals 12/5. Divide and you get 2 and 2/5. 2/5 of an hour is 24 minutes.</P><P>your answer is 2 hours and 24 minutes
goldie45 Posted - 22 October 2006 0:53  Show Profile
Georgene,<BR>Thank you so much for helping me! I've tried that method on a couple problems just like it and finally got the hang of it!
Filksinger Posted - 25 October 2006 1:22  Show Profile
There is another way to look at it that some people find easier. </P><P>Find the smallest common multiple of Sally's painting time (4 hours) and John's painting time (6 hours). The smallest number that can be divided by both 4 and 6 is 12. In 12 hours, Sally will finish 3 houses, and John will finish 2.</P><P>So, in 12 hours, or 720 minutes, John and Sally would have finished a total of 5 houses. This means they would finish one house in 720/5 = 144 minutes, or 2 hours 24 minutes.

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