# 4Tests Forums

 Forums • GED • How do you solve.. Thread Closed
 Author Topic goldie45 Posted - 2 October 2006 0:21 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 Can anyone explain this answer? I too would like to see how it is worked. Thank you. Georgene Posted - 12 October 2006 19:20 I think that I have it figured out.

Set this problem up as a fraction that you will add, then you will divide the smaller number into the larger number (time).

Number of people 1 1
_____________= ___ + __
time 4 6

Find the commom denominator (12) and add the fractions.

3 2 5
__ + ___ = ___
12 12 12

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.

I solved for 2/5 of an hour by setting it up as a proportion.

2 ?
__ = ___
5 60

Cross multiply 2 x 60 (equals 120), and divide by 5. 120 divided by 5 = 24. Georgene Posted - 12 October 2006 19:21 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 I'm still a little confused Georgene Posted - 17 October 2006 16:33 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.

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.

your answer is 2 hours and 24 minutes goldie45 Posted - 22 October 2006 0:53 Georgene,
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 There is another way to look at it that some people find easier.

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.

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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