4 boys can scrub the whole floor of a school hall in 2 and 1/2 hours. How long will it take 5 boys to scrub the floor at the same rate
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5/4 the people, so 4/5 the time: 2 hrs
To solve this problem, we can first find the rate at which a single boy scrubs the floor by dividing the total time taken by the number of boys.
If 4 boys can scrub the whole floor in 2 and 1/2 hours, the total work done is 2.5 hours.
So, the rate at which 4 boys work is:
4 boys / 2.5 hours = 1.6 boys/hour
Now, let's find the time it will take for 5 boys to scrub the floor at the same rate.
If 1 boy can do the work at a rate of 1.6 boys/hour, then 5 boys can do the work 5 times faster.
So, the total time for 5 boys to scrub the floor is:
2.5 hours / 5 = 0.5 hours
Therefore, it will take 5 boys to scrub the floor in 0.5 hours (or 30 minutes).
To solve this problem, we can use the concept of "man-hours." The total work to be done is scrubbing the whole floor of a school hall. In this case, we have 4 boys who can complete the work in 2.5 hours.
To find out how long it will take 5 boys to complete the same amount of work, we need to consider that the total work remains constant. The formula we can use is:
(Number of boys) x (Number of hours) = Total man-hours
Using this formula, we can find the total man-hours for the 4 boys:
4 boys x 2.5 hours = 10 man-hours
Now, let's determine how long it will take 5 boys to complete the same amount of work:
5 boys x (unknown number of hours) = 10 man-hours
To find the unknown number of hours, we can rearrange the formula:
(Unknown number of hours) = 10 man-hours / 5 boys
Now, let's solve for the unknown number of hours:
(Unknown number of hours) = 10 man-hours / 5 boys
(Unknown number of hours) = 2 hours
Therefore, it will take 5 boys approximately 2 hours to scrub the floor at the same rate as the 4 boys.