Two girls take two hours to sweep the school compound, if the second girl alone takes three hours to sweep the same compound working at the same rate how long does first girl take if she works?

If the second girl alone takes three hours to sweep the school compound, then the rate at which she works is 1/3 of the compound per hour.

Since both girls working together can sweep the compound in 2 hours, their combined rate is 1/2 of the compound per hour.

Let x be the time it takes for the first girl to sweep the compound alone. Therefore, her rate is 1/x of the compound per hour.

Since the combined rate of the two girls is the sum of their individual rates, we can write the equation:

1/x + 1/3 = 1/2

Multiplying through by 6x to clear the fractions:

6 + 2x = 3x
6 = x

Therefore, the first girl takes 6 hours to sweep the school compound alone.

Step 1: Find the work rate of the two girls combined.

Since they take 2 hours together:
Work rate of both girls = 1/2 compound/hour

Step 2: Find the work rate of the second girl alone.

Since she takes 3 hours alone:
Work rate of second girl = 1/3 compound/hour

Step 3: Find the work rate of the first girl alone.

Work rate of first girl = Work rate of both girls - Work rate of second girl
= 1/2 - 1/3
= 1/6 compound/hour

Step 4: Find the time it takes the first girl to complete the task alone.

Time = Work / Work rate
Time for first girl = 1 compound / (1/6 compound/hour)
= 6 hours

Therefore, the first girl would take 6 hours to sweep the school compound if she worked alone.