How Much did the Tree Grow?

Date: 11/07/2001 at 19:46:11
From: Robert Blokzyl
Subject: Subtracting 2-Digit Numbers

A white pine was 16 m tall in 1962.  It was 20 m tall in 1965. It is 
now 34 m tall.  How much has it grown since 1962?

I added 16 and 20 and 34 and subtracted that from 16.  The answer is 
54.  I am not sure if that is correct.  It doesn't seem right to me.

Date: 11/08/2001 at 12:39:46
From: Doctor Ian
Subject: Re: Subtracting 2-Digit Numbers

Hi Robert,

Sometimes a picture can help:

                       Growth
                       since
                 34m   1962
                  |     |
                  |     |
          20m     |     |
   16m     |      |     |
    |      |      |
    |      |      |
    |      |      |
    |      |      |
   1962   1965   now

In fact, it makes no difference how tall the tree was in 1965.  The 
relevant information in the problem is 

  A white pine was 16 m tall in 1962.  It is now 34 m tall.  
  How much has it grown since 1962?

That's part of what this problem is supposed to teach you - that 
sometimes a problem will contain information that isn't relevant, 
e.g., 

  Bob and Sam drove a yellow Mercedes convertible from New York 
  to Los Angeles, a distance of 3900 miles.  They stopped for coffee
  28 times, and stopped to use restrooms 19 times.  They spent 
  $125 on food, and listened mostly to the Beach Boys and 
  Nirvana while driving. They were stopped for speeding twice,
  but were able in each case to talk the police officer out of
  giving them a ticket. The price of gas varied between $1.29 
  and $1.56 per gallon. If the trip took 78 hours, what was their
  average speed? 

This is sort of an extreme example, but the only relevant information 
is this:

  Bob and Sam drove a distance of 3900 miles. If the trip took 
  78 hours, what was their average speed? 

I hope this helps.  Write back if you'd like to talk about this some 
more, or if you have any other questions. 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/