1/8-1 hour
2/8- 2 hours
2/8+1/10x=1
1/10x=6/8
x=7.5 hrs
2/8- 2 hours
2/8+1/10x=1
1/10x=6/8
x=7.5 hrs
rate of first crew = 1/8
job done by first crew in 2 hours = 2(1/8) = 1/4
job left to be done = 1 - 1/4 = 3/4
rate of second crew = 1/10
time needed for 2nd crew to finish
= (3/4) / (1/10)
= 30/4 hrs or 7.5 hrs
Let's assume that the first crew's work rate is represented by "x," which means they can clean 1/8th of the building in one hour.
Similarly, if the second crew's work rate is represented by "y," they can clean 1/10th of the building in one hour.
Since the first crew worked for 2 hours, they'll have completed 2 * x = 2/8 = 1/4th of the building.
To finish the remaining 3/4th of the building, the second crew will take (3/4) / y hours.
To find the time taken by the second crew, we need to substitute the value of y:
[(3/4) / (1/10)] = (3/4) * (10/1) = 30/4 = 7.5 hours.
Therefore, it will take the second crew 7.5 hours to finish cleaning the building after the first crew leaves.
We know that the first crew takes 8 hours to clean the building and the second crew takes 10 hours to clean the same building. This gives us the rates of work for each crew:
First crew's rate = 1/8 (one building per 8 hours)
Second crew's rate = 1/10 (one building per 10 hours)
Since the first crew worked for 2 hours and completed a portion of the cleaning, we can calculate their contribution to the total work:
First crew's work = Rate × Time
= (1/8) × 2
= 1/4 (one-quarter of the building)
Now, we need to find out how long the second crew will take to finish the remaining three-quarters of the cleaning. Let's denote the unknown time as "t" hours.
Second crew's work = Rate × Time
= (1/10) × t
= t/10 (tenth of the building per hour)
Since the first crew completed one-quarter of the building, the second crew will be responsible for the remaining three-quarters. So, we can set up the equation:
Second crew's work = 3/4 (remaining work)
t/10 = 3/4
To solve for t, we can multiply both sides of the equation by 10:
t = (3/4) * 10
t = 30/4 or 7.5
Therefore, it will take the second crew 7.5 hours (or 7 hours and 30 minutes) to finish cleaning the building.