Question

dora has three candles, which will burn for 3, 4 and 5 hours, respectively. if she wants to keep two candles burning at all times, what is the greatest number of hours she can burn the candles? (dora has a clock that she can use to time the candles, and she can blow out any candle whenever she wants.)

Answer 1

6 hours

Explanation:

Dora wants to know how long she can keep 2 candles burning at all times if she has candles of lengths 3, 4, and 5 hours. She can start or stop burning any time.

Total time

The candles have a total burning time of 3+4+5 = 12 hours.

2 at once

If two are burning at once, the longest time they can burn is 12/2 = 6 hours. To ensure this is correct, we need a plan for the burning that will allow this duration to be achieved.

Plan

For the 1st hour, burn the 3- and 4-hour candles. (Blow out the 4-hour candle.)

For the next 2 hours, burn the 3- and 5-hour candles. (The 3-hour candle is done.)

For the last 3 hours, burn the 4- and 5-hour candles.

Only the 4-hour candle is stopped and started again after it is lit. the other two remain lit for their duration.

Dora can burn 2 candles at once for a total of 6 hours.

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Additional comment

The pairings (3, 4 for 1 hour), (3, 5 for 2 hours), (4, 5 for 3 hours) can be done in any order. In different orders, different candles need to be restarted.

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