To solve this problem, you can break it down into steps:
Step 1: Determine the rate at which each crew completes the work.
The first crew can frame a single story house in 7 days, so their rate is 1/7 houses per day.
The second crew can frame a single story house in 5 days, so their rate is 1/5 houses per day.
Step 2: Determine the total amount of work done in the first two days.
Since the first crew started working first, they would have completed work for 2 days. Therefore, in those 2 days, the first crew would have completed 2 times their daily rate, which is (2/7) houses.
The second crew arrived 2 days after the first, so they have not done any work during these 2 days.
Step 3: Determine the rate at which both crews work together.
The combined rate of both crews working together is the sum of their individual rates. So, the combined rate would be:
1/7 + 1/5 = (5 + 7) / (7 * 5) = 12/35 houses per day.
Step 4: Calculate the time required to frame a single house when both crews work together.
Now that we know the combined rate of both crews, we can determine how long it will take to frame a single house. We can use the following formula:
Time = Amount of work / Rate
Since we need to frame 1 house, the amount of work is 1. So, the time required would be:
Time = 1 / (12/35) = 35/12 days.
Thus, it will take approximately 2.92 days (or about 2 days and 22 hours) to frame a single story house if the second crew arrived 2 days after the first.