It takes thirty kids six hours to build a man-sized sand castle.How many kids were there if the same game took only two and a half hours?

To solve this problem, we need to understand that the time it takes to build the sand castle is inversely proportional to the number of kids building it. This means that if more kids are building the castle, it will take less time.

Step 1: Identify the initial number of kids and the time it took them. In this case, it's 30 kids and 6 hours.

Step 2: Identify the new time. In this case, it's 2.5 hours.

Step 3: Set up a proportion to solve for the new number of kids. The proportion is (30 kids / 6 hours) = (x kids / 2.5 hours).

Step 4: Solve for x. Cross-multiply to get 30 kids * 2.5 hours = 6 hours * x kids.

Step 5: Simplify to get 75 = 6x.

Step 6: Divide both sides by 6 to solve for x. x = 75 / 6 = 12.5.

However, since we can't have half a kid, we round up to the nearest whole number. So, it would take approximately 13 kids to build the sand castle in 2.5 hours.