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June 11th, 2015, 01:56 PM   #1
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Question No idea how to solve this

This actually really frustrated me. I'm probably a 'just below-average' math student. And this word problem is really difficult.

If someone can solve this by showing there work, I'd seriously greatly appreciate it. This allows me to look at what you did and how you got your answer.

Here's the word problem.

"Batman has been thrown into an airtight cell by the Arkham Knight!

He has two tools that will cut through the six inch thick metal walls off the cell. Batman needs to cut through to reach fresh air before he suffocates.

The explosive gel blasts through the metal at a rate of 3cm/blast, But burns oxygen at a rate of 112,000 CC/Blast.
It takes 28 seconds to spray, arm and detonate an explosive gel blast.

The blowtorch cuts through the metal at a rate of 1cm/minute, but burns oxygen at a rate of 37.06 Litres/minute.

Batman takes up a space of 0.094m^3 and has reduced his breathing to consume oxygen at a rate of 5 litres/minute.

Which tool should Batman use to escape? "
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June 11th, 2015, 07:37 PM   #2
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Quote:
Originally Posted by ThatDude55 View Post
The explosive gel blasts through the metal at a rate of 3cm/blast, But burns oxygen at a rate of 112,000 CC/Blast.
It takes 28 seconds to spray, arm and detonate an explosive gel blast.

The blowtorch cuts through the metal at a rate of 1cm/minute, but burns oxygen at a rate of 37.06 Litres/minute.

Batman takes up a space of 0.094m^3 and has reduced his breathing to consume oxygen at a rate of 5 litres/minute.
One use of the explosive gel will take 28 seconds and 112,000 CC + 28/60 * 5 L. Doing the unit conversion this is about 114.3 L. An equivalent use of the blowtorch takes 3 minutes and consumes 37.06 L + 3*5 L = 52.06 L. So if oxygen is the limiting factor the blowtorch is better, though the gel is better if you're short on time and have plenty of oxygen. It sounds to me like the blowtorch is better in this scenario.
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June 11th, 2015, 07:49 PM   #3
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Wall thickness = 6 inches = 15cm

Tools available:

1. Explosive blast:
a) Takes 28 seconds to prepare
b) cuts at the rate of 3cm/blast
c) consumes oxygen at the rate 112,000 cc/blast

It takes 5 blasts to escape. So...
Oxygen consumed by 5 blasts = 112,000 * 5 = 560,000 cc
total time taken = 5 * 28 = 140 seconds
oxygen consumed by Batman = 5L/60 seconds * 140 seconds = 12,000 cc

Total oxygen consumed if Batman uses the explosive blast = 560,000 + 12,000 = 572,000cc

2) Blowtorch:
a) cuts at 1cm/minute
b) burns oxygen at 37.06L/minute

It takes 15 minutes to cut through the wall.
Batman consumes = 5 L/minute * 15 minutes = 75L = 75,000cc of oxygen
Oxygen consumed by blowtorch = 37.06L/minute * 15 minutes = 555,900cc

Total oxygen consumed if blow torch is used = 75,000 + 555,900 = 630,900cc

Assuming that oxygen is the limiting factor...
Oxygen consumed using explosive blast (572,000cc) < oxygen consumed using blowtorch (630,900cc)

So, Batman should use the explosive blast.
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Last edited by shunya; June 11th, 2015 at 08:02 PM.
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June 12th, 2015, 07:44 AM   #4
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Oops -- I forgot that the blowtorch rate was per minute rather than per 3 cm!
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June 23rd, 2015, 11:36 AM   #5
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Don't forget the size of the room!

There is only 94L of oxygen to begin with. Both techniques use too much of the oxygen to be worth using.
I think it would be wise for Batman to wait for help

Last edited by skipjack; June 23rd, 2015 at 12:41 PM.
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