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Question 1123313: A line segment has length 36 cm. It was divided into four unequal parts. If the distance between the midpoints of the first and the fourth parts is 30 cm, what is the distance between the midpoints of the second and the third parts?
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
Consider very first and very last of the four subdivision segments.
The midpoints divide each of these two segments in two equal parts.
Since the total length of the original segment is 36 cm and the distance between two mentioned midpoints is 30,
it means that half of the first segment and half of the last segment have combined length of 36-30 = 6 cm.
Hence, the total length of these two segments is 2*6 = 12 cm, leaving 36 - 12 = 24 cm for the combined length of the second and the third subdivision segments.
It implies that the distance between the midpoints of the second and the third parts is half of 24 cm, i.e. 12 cm.
Answer. The distance between the midpoints of the second and the third parts is 12 cm.
Solved.
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