A 100-meter rope is cut so that the shorter piece is two-thirds the length of the longer piece. What is the length of the shorter piece?A10 metersB30 metersC40 metersD45 metersSUBMIT
Question
A 100-meter rope is cut so that the shorter piece is two-thirds the length of the longer piece. What is the length of the shorter piece?A10 metersB30 metersC40 metersD45 metersSUBMIT
Solution
Let's denote the length of the shorter piece as S and the length of the longer piece as L.
According to the problem, we have two equations:
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S + L = 100 (since the total length of the rope is 100 meters)
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S = 2/3 * L (since the shorter piece is two-thirds the length of the longer piece)
We can solve these equations step by step:
First, substitute the second equation into the first to get: 2/3 * L + L = 100
This simplifies to: 5/3 * L = 100
Solving for L gives: L = 100 * 3/5 = 60 meters
Substitute L = 60 into the first equation to get: S + 60 = 100
Solving for S gives: S = 100 - 60 = 40 meters
So, the length of the shorter piece is 40 meters. The answer is C) 40 meters.
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