Question

how long can it swing?

	height dropped from (centimeters)	time swung (seconds)
test 1	10 cm	25 sec
test 2	20 cm	?
test 3	30 cm	72 sec

options: 49 sec, 12 sec, 19 sec, 83 sec

Explanation:

Step1: Analyze the trend

We observe the relationship between height dropped and time swung. As height increases from 10 cm (Test 1) to 30 cm (Test 3), time increases from 25 sec to 72 sec. For Test 2, height is 20 cm (midway between 10 and 30). We expect time to be midway or follow a pattern. Let's check the options. 25 (Test1) <? < 72 (Test3). So 49 is between 25 and 72, 19 and 12 are less than 25, 83 is more than 72. So 49 is the most reasonable.

Step2: Confirm the pattern

The height doubles from 10 to 20, and triples from 10 to 30. The time at 10 is 25, at 30 is 72. The increase from 10 to 30 (20 cm increase) leads to 47 sec increase (72 - 25). So for 10 cm increase (10 to 20), we can estimate around half of 47, so 25 + 24 = 49, which matches the option.

Answer:

49 sec