johnnybravo86 wrote:
Please help me solve this problem
A husband and wife, started painting their house, but husband left painting 5 days before the completion of the work. How many days will it take to complete the work, which the husband alone would have completed in 20 days and wife in 15 days?
a) 40/7 b)50/7 c)75/7 d) 55/7
It's a multiple step problem: 1) figure out how many days (D) it would take the husband and wife to complete the job working together, 2) figure out how much of the house would be painted in D-5 days, 3) figure out how long it would take the wife to paint the remaining portion
1. How many days would it take the husband and wife to complete the house working together?
Each day, the husband can paint 1/20 of the house, and the wife can paint 1/15 of the house, so combined they can paint (1/20 + 1/15 = 7/60) of the house.
At that rate it would take them 60/7 days to complete the house. (7/60 house/day * 60/7 days = 1 house)
2. How much of the house can they paint in D-5 days?(D-5 = 60/7 - 35/7 = 25/7) If working together they paint 7/60 of the house per day, then in D-5 days they could paint:
7/60 house/day * 25/7 days = 175/420 = 5/12 of the house will be painted in D-5 days.
3. How long will it take the wife, working alone, to paint this portion of the house?The wife can paint 1/15 of the house each day, and there is 5/12 of the house that needs to be painted, so it would take her (5/12) / (1/15) = 25/4 days.
Well, I've checked my math a few times and came up with the same answer, which isn't one of the options presented. Where did the question come from?
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