Problem
You have two ropes and a box of matches. Each rope takes exactly one hour to burn, but they may not necessarily burn evenly – i.e., the first half might burn in the first 10 minutes and the second in the remaining 50). Whats the time you can measure using the 2 ropes?
A)1 hr
B)30 min
C)45 min
D)15 min
Solution Approach:
Light one end of the rope .Measure the time taken for complete burning=1 hr
Light the other rope from both ends.Time taken till the burns meet=30 min
T=60+30/2=45 min
What you need to do is light one from both sides, and simultaneously light the other one from only one side. When the first burns completely, 30 minutes have passed, and the second will be halfway through its burn. Then you light -that- one from the other end, halving its remaining burn time to 15 minutes, and when that one is done you'll have 45 minutes exactly.
You have two ropes and a box of matches. Each rope takes exactly one hour to burn, but they may not necessarily burn evenly – i.e., the first half might burn in the first 10 minutes and the second in the remaining 50). Whats the time you can measure using the 2 ropes?
A)1 hr
B)30 min
C)45 min
D)15 min
Answer: All of the above
Solution Approach:
Light one end of the rope .Measure the time taken for complete burning=1 hr
Light the other rope from both ends.Time taken till the burns meet=30 min
T=60+30/2=45 min
What you need to do is light one from both sides, and simultaneously light the other one from only one side. When the first burns completely, 30 minutes have passed, and the second will be halfway through its burn. Then you light -that- one from the other end, halving its remaining burn time to 15 minutes, and when that one is done you'll have 45 minutes exactly.
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