It takes 8 hours for one crew to clean an office building. It takes a second crew 10 hours to clean the same building. If the first crew works 2 hours and leaves and the second crew takes over to complete the job, how long will it take the second crew to finish cleaning the building?
let the work to be done be 1 unit
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
1/8-1 hour
2/8- 2 hours
2/8+1/10x=1
1/10x=6/8
x=7.5 hrs
To find out how long it will take the second crew to finish cleaning the building, we need to calculate the remaining time needed to complete the job after the first crew leaves.
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.
To find out how long it will take the second crew to finish cleaning the building, we can use the concept of work and the inverse relationship between time and the rate of work.
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.