Tuesday, 24 June 2014

Bearapocalypse final

A week ago I posted a numeracy problem in which a water tank needed to be filled by two people.  It was imperative that the tank be filled within two hours or less or the world would essentially end.  You can read the post here and have a go at the problem.

One person could fill the tank in three hours (Karl).  The second person could fill it in five hours (Larry).  The question was:  If they work together how long will it take them?

This is a TOUGH question.  But here are some tips.

  1. If fractions freak you out just don't use them.  Turn them into decimals immediately by dividing the top number by the bottom on a calculator.  Easy.
  2. If you want to keep fractions but hate adding them - just type the sum into into Google and you get your answer!  Yes, Google does add fractions.  Just type, 'one-third plus one-eighth'.  Cool huh.

Okay - the problem solved my way -  Think about how much of the water tank Karl and Larry will fill in one hour.

Here is how I approached it.

1.  In one hour how much of the tank does Karl fill?.  Answer one/third (or .333)
2.  In one hour how much of the tank does Larry fill?.  Answer one/fifth. (or .2)

So if these two chaps work together, then in one hour the tank has one/third plus one/fifth in it (or .333 + .2 = .533).

The answer in fraction language is eight-fifteenths or if you want to turn it into decimals = 0.533.

Okay, so in one hour Karl and Larry have it a little over half full.  So there you have it - if they can fill it above halfway in one hour then it is definitely full in two.  Don't over think it.  Will they be back in two hours? Yes.

If you want to be a genius you may want to work out exactly how many minutes it will take them to fill the tank.  Well, it took one hour (60 min) to fill eight-fifteenths.  So how long to fill up seven-fifteenths?

I guess we have to work out how many minutes each of those eighths took?  60 divided by 8 = 7.5.  So 7.5 minutes to fill one-fifteenth.  How many minutes to fill fifteen-fifteenths?  15 times 7.5 = 112.5 min.

Okay, clearly this is a tough one. But keep in mind - the future of the human race depended on it.  So when the apocalypse happens are we all going to look at each other and say 'Who's good at maths?'.

I know in every movie there is always that one geeky guy who can do the math - but what if the job falls to you?

1 comment:

  1. This is a great series... At some stage you should do a post that summarises each one in one sentences the links back to the original post. Like a menu.