One crew can frame a single story house in 7 days, while a second crew can do it in 5 days. how long will it take to frame a single house if the second crew arrived 2 days after the first.
Im having problems setting it up with the 2 days after the first
Let the completed job be represented by 1
The first crew worked for 2 days, so they did 2/7 of the job.
This leaves 5/7 of the job to be finished by the combined work of the two crews
rate of first crew = 1/7
rate of 2nd crew = 1/5
combined rate = 1/7 + 1/5 = 12/35
let the time remaining for the job to be done be t
(12/35) t = 5/7
t = 5/7 * 35/12 = 25/12 hrs
= 2 hours and 5 minutes
check:
2(1/7) + (25/12)(12/35)
= 2/7 + 5/7
= 1 , the job is done
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.